Memory might be the most important with perhaps a 2GB requirement just guessing. You'll have to test, it's how we basically figured out the minimum requirements for Mozilla and there are people running Mozilla carefully on PII's.
I'd also guess that if they get it running in multi-process mode, there will be a switch or such (the Simple Browser seems to use an environment variable) to put it in single process mode which should require less CPU.
Is there a C2D Xeon that would plug into that board? Old Xeon's are fairly cheap and at one point I had a Pentium 4D at 2.8Ghz, swapped in a 1.86GHz C2D and got a performance boost as well as using half the power. Later I swapped in a C2D extreme at 2.8Ghz and it flew.