It would, most likely, be cheaper to just buy a new one. Parts, especially circuit boards, are super expensive to replace.
I think our microwave is dying...it's just not heating things up like it used to...is there a way to repair it?
Hippy is right. There are some appliance repair places that might be able to help you but microwave prices have went way down and it is easier to just replace it. If you have a Sears store near you? Try them as they have much better prices that Lowe's and the others and they came and removed my old one and installed the new one for free.
If it is not heating it is probably the magnetron that is going bad, and it is much cheaper just to buy a new.
As has been said, the problem is the magnetron (probability = 99%)
Some magnetrons cost more than a a new oven would. ($60 to $100 on line)
A reliable, good sized microwave can be had for about $70.
The last time this happened to me, I found a new one for much less than the estimated repair cost. Take a peek online.
you should buy a new one.
