The Paula for an A2000 is not too hard to find. In fact, you can use a Paula from an A500, which are very common on Ebay (and not too expensive). I'm sure some Amiga dealers also have the Paula chips themselves for sale.
Actually, I think the Paula chip remained virtually unchanged in all the Amiga models....so you might be able to use any Paula chip in your A2000. But check into this before you use one not from an A500/2000.
Also, try reseating your Paula chip (just press down on it after you have grounded yourself to prevent static electricity from ruining it). It might have become unseated through the years (temperature extremes, vibration, etc.).