Unfortunately for you, CCDs are the most expensive component of the camera, and it's extremely unlikely that 3rd party repair shops will stock such spares. It's still possible to send to shops to check out mechanical problems (like the shutter problem - maybe needs lubricating?), but when it comes to electronics, the official service centre is your only option.
That said, out-of-warranty repairs are expensive, especially for an older model A2, so it probably won't be worth it. I think it's better that you start looking for a replacement for your A2. Still, no harm taking your camera down to Sony Service Centre and see what they have to say about it.
Best of luck!