The most common problem with any electronic component pulled from a decade long storage situation is dis-use is actually much harder on electronics than is constant use. Lubricants begin to dry up when they have been placed in storage and electronic parts can drift to the point of failure. Somewhat surprisingly, failure doesn't typically occur on first use but waits for awhile ( a few weeks is common) before the old gear simply shows it age and its lack of attention over time.
Now, your camera may work indefinitely or not so indefinitely. No one can predict such things.
Your camera is/was, however, a less expensive compact from Canon's line of products. How do you build a less expensive product? By using less expensive parts usually. Expensive parts don't necessarily equate to longevity since higher quality typically comes with tighter tolerances and, at times, it is quite literally the "slop" of lower tolerances that assists older components in staying together.
So, IMO use your camera for now but look for something newer and more up to date in the future. The issues of rather slow auto-focus speeds have been mentioned. Newer cameras respond much more rapidly and accurately to your input. That can mean the difference between getting the shot and not. And, certainly, with a long shutter lag after pressing the release, camera shake is all too common. Camera shake results in blurred images.
The image file format used by your camera is ten year old technology Jpeg. If you get serious about your photography, you probably wouldn't use Jpeg files. The "compressed" nature of a Jpeg file means the camera has controlled a good deal of your final image quality and you are left with little to do to make corrections or improvements to the image.
Jpegs created with today's technology are generally considered to be adequate for posting shots on the web or on social media. Smart phones today shoot in Jpeg. Most smart phones of today would have higher quality file management than your current camera is capable of producing.
Seldom would a "serious" photographer print from their camera's Jpeg file. Therefore, when you go hunting for a new camera, be on the look out for a model that includes "RAW" capture as a file format.
The LCD screen on your present compact is very small and the image quality displayed via the LCD is not so great due to a fairly low pixel count. This is another area where a modern smart phone would provide higher quality than you are getting from this camera. The tiny screen and low resolution image makes judging your shots rather difficult compared to the larger LCD's of today with considerably higher resolution. That applies to a phone's camera or a modern DSLR/compact. And, there are several modern, somewhat less expensive "compact" cameras that can turn out very high quality images, even in low light conditions.
The fixed lens on your older compact does answer a lot of your question whether cameras and lenses have improved over time.
First, with a single fixed lens, you may find you are never quite capable of finding the desired focal length for the shot you see in your head. Whether you wish to get in very close or shoot at great distances, these are the limitations of your current camera; it won't do either well. And you are rather "stuck" with that one single lens for either style of photography.
Second, you are using a digital camera. Consider where other digital products were at the time of your camera's design and where they are now. I can't think of any digital product that is built today that isn't faster and "more powerful" than a similar component from a decade prior. To your camera this means, yes, today's digital cameras have come a long way in improving image quality. Digital cameras rely on "error correction" circuits just as a digital music player would. The more powerful digital circuits found in today's cameras makes the camera and the lens less prone to errors occurring in the final image.
Now, just as I can't predict what you consider to be sufficient image quality, I can't say whether you will immediately notice any difference in a photo shot with your current camera and a brand new DSLR.
As with digital audio components, it is often a matter of experience with the "better" product which informs the user of the limitations of older and less expensive equipment. But, technically, yes, I would say today's digital cameras, even on the lower end of the price range, have come a long way since your camera was designed.
My guess would be, if you took some photos with more colorful subjects filling more of the frame and then you blew those images up on your computer monitor, you would begin to see the limitations of your camera in both color accuracy and in image sharpness once you looked beyond the center of the frame. Corner to corner sharpness and color resolution are the result of today's more powerful digital circuitry.
In the end, however, these are only technical considerations and good photography comes more from the photographer than from the gear.
Your current camera is perfectly acceptable for use in establishing, first, your continued interest in photography. Not everyone who picks up a camera sticks with it. There are rules and techniques to master and some people find them to be burdensome. There's little point in investing in another camera if it will end up sitting as long as your current camera has.
Your current camera has a sufficient amount of user control which can be exploited to move you away from simply shooting every image in full automatic mode. The TV and Av modes are where a more imaginative photographer will spend most of their time with their camera.
Many photographers have a difficult time grappling with composition and exposure values. Your present camera is adequate for "composition" lessons.
If you do not get frustrated by the equipment's ability to place in a frame what you see in your head as "the shot", then you are on a good road to learning composition.
Exposure is covered adequately for now by your camera's Av and Tv modes. You can begin to learn the basics with your camera.
As mentioned ISO values - those higher values you would require for low light photography - are far superior in today's cameras. The "exposure triangle" all photographers must use relies on the ability of the equipment to raise ISO values in certain conditions. Nudge your current camera upward even slightly and you will begin to see digital noise occurring in your shots. This noise will be ever more evident as you increase the size of the display or print. This is yet another area where a modern smart phone will out do you current Canon.
Therefore, use your present camera as the learning tool you have at your disposal. Most of what makes a photograph interesting can be accomplished with this camera.
And "new" doesn't necessarily mean it will be the best for you.
Do your research and gather ideas regarding what is important to you and your "style" of photography. If you stick with this, you will certainly want a more advanced camera.
You can then keep using this one as a day to day carry around that will be with you when the shot appears. Better to carry a less expensive version of a camera around for that than to always haul out the big guns.