My 60D refuses to focus in anything but auto. I mostly like to use the "P" mode. I have some great point and shoot cameras, but paid big bucks if this is all this guy will do.
Good news! The fact that the camera CAN focus in auto-mode is a clue as to what's going on and also helps back up that there's probably nothing wrong with the focus system.
When you put the camera into full automatic mode, the camera switches off a lot of configuration changes YOU may have set and locks out user control. In other words... when the computer is in charge, everything is fine.
When you leave auto-mode, you have the ability to override the focus system in a few ways.
1) You can choose whether to allow auto-focus point selection (the camera can use any of your 9 cross-type AF points) - OR - YOU can force the camera to use a SPECIFIC auto-focus point. In the far upper-right corner of the camera (as you view the back) is a small button which puts the camera into focus point selection mode. It will only work if the camera is NOT in auto-mode. Take the camera out of auto (for example, use P (Program) mode.) Push the AF selection button then roll the main dial while looking through the viewfinder and you'll see the camera highlight each focus point as you turn the dial. There's a point where all 9 points will light up (auto-selection mode where the camera can use any point it wants.)
2) You can also choose whether to put the camera into AI Servo mode vs. One Shot focus mode. But these come with side-effects. In "One Shot" mode, the camera uses something called "Focus Priority". This means when you press the shutter button completely, the camera's priority is to first FOCUS the shot and THEN shoot. The camera will refuse to shoot if it cannot lock focus on something (hence focus priority). However, once the camera DOES lock focus the focus system will stop trying to focus and will wait for you to shoot. If you move or if your subject moves... the camera will NOT update the focus to compensate.
If you switch the camera to "AI Servo" mode (usually used in sports or action photography), the camera focus system behavior changes in several ways. First... it will focus continuously for as long as you keep half-pressing the shutter button... if your subject moves the focus will update to compensate. BUT... the camera also uses a mode called "Shutter release priority". This means when you fully press the shutter button... the camera WILL take the shot immediately. In fact... the shutter has so much priority that the camera will take the shot even if nothing is focused at all. The trick in this mode is to half-press until the camera focuses to your satisfaction and then finish pushing the shutter button all the way.
3) Understand how your camera focus system "thinks". The Canon AF system is programmed so that IF you allow the camera to choose which any focus point, then the focus point it will use is not actually random. it will always pick the focus point which is able to lock focus at the NEAREST distance to the camera. So if you've got a shrubbery in the foreground and a person in the background and you want the camera to focus on that person and leave the shrubbery out of focus... you'll be disappointed when the camera locks onto the shrubbery... because it's closer. This, btw, is WHY the camera lets you override which AF point it uses.
Watch this three part video series... it's EXTREMELY helpful:
That's part 1 of 3... parts 2 and 3 are below.
https://www.youtube.com/watch?v=3_F7lCvp5DI
https://www.youtube.com/watch?v=1WTWiN9kLts
Good luck!
One last thing... if you flip the camera into "live view" mode..... a COMPLETELY different focus system is used. If you suspect a problem with the phase-detect focus system (that's the normal focus system used in a DSLR) then switch to "live view" mode to test it because this uses the camera's contrast-detect focus system and the two are actually not related.
