Assuming you're not shooting in AUTO mode......................................
On a Nikon, when you're in AF-S or AF-A, will not shoot a picture without AF confirmation. It's common with any autofocus camera in indoor situations where the AF action will be slower to lock.
The D70 uses an electronic shutter, the mechanical shutter won't go above 1/90th of a second. Unless you've put over 100,000 clicks on the camera (which I doubt, most people don't ever get close), I doubt there's anything wrong with the shutter.
Unless you're doing long (as in minutes) exposures often, the CCD shouldn't be getting more noisy over time, check to see if Auto ISO is on.
I doubt there's anything wrong with the camera. Usually components stop working all together instead of "slowing down". My guess is you got your hands on a newer camera and saw just how old the D70 is.