What are your other specs? Specifically, what motherboard and PSU are you using? What resolution/detail levels are you trying to run it at? Do you have an aftermarket cooler for overclocking/unlocking? Have you tried overclocking/unlocking?
Unfortunately, $100 isn't much to play with. That $100 isn't going to buy you much. So I'd recommend trying to lower some of the details a little to see if the problem is fixed. If that doesn't help, you're definitely looking at some upgrades.
Like I said, there isn't much you can get for under $100 that'll help. You could drop $100 on a
X4 640, but that wouldn't likely give you a large performance gain. To get a much better CPU, you'd need $140-150 for the X4 955. If I remember correctly, BC2 does like CPUs with more cores, but I don't think it's enough to warrant a $100 expenditure on an older CPU.
If you haven't tried overclocking, I'd suggest picking up an aftermarket HSF (assuming you don't have one yet). Look at either the Coolermaster Hyper 212 Plus ($30) or Scythe Mugen 2 Rev. B ($40). They'll fit in the vast majority of regular sized cases. That would be a cheap way to get some more performance.
Other than that, about the only thing you can add is a second
HD 5770. It's exactly $100 if you count the rebate. Of course, you'll have to already have a motherboard with a second PCIe 2.0 slot running at 8x or higher and a 650W or larger PSU.
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