If your happy with your cpu speed as is, then its no problem.
(edit) the radeon 3850 doesnt "require" any specific cpu speed, but its performance would be limited by your cpu's, eg - you may well find games where adding the new gpu gives only 1-2 fps more because the cpu's are working 100% and gfx isnt, conversely in same games you may get more fps gain as the cpu's were idle, but old gfx was at 100%. this can ofc be countered by just turning the fsaa up, same/much better performance in all games (depending on the age of game) with better graphics in all.
as stands: your 2*athlon mp 2600's are roughly equivelant to a (theoretical) 3000+ athlon x2, - that would be dualcore 1.6ghz. (ive tried to account for the loss of dual channel, X-bar, imc and the athlon 64 alu/fps improvements in the 400mhz actual core speed drop)
this is
substantially faster than any atom cpu.
but a lot slower than the current cpu's on offer.
your cheapest cpu upgrade would be to move to a 2nd hand socket 939 system, as this would take your existing ram and agp boards are fairly common. meaning just a board + cpu. however this tech is several years out of date of and on its own. you should consider a move to AM3, perhaps pairing some cheap 1066 DDR3 sticks with a athlon x2 250 and your choice of graphics (anything over and including the 3400 series should be faster in most cases than your current gpu)
this is, ofcourse, if you are not happy with your pc as it is. if your happy, dont change
