A burning smell is never a good sign!
If you have cooked the CPU then it's very likely that a replacement CPU from Ebay (as Al said) will sort it out, try and get one that comes with the required thermal paste for mounting the heatsink to it, or ensure you buy some at the same time.
There is a slim chance it may have damaged the motherboard. But realistically the only way to find out is to try a new CPU.
A little more info than just it's a HP would help though, because if you are going to buy a new CPU then it may be possible for you to fit a slightly better one but this depends entirely on exactly what you have at the moment.