As an aside, I completely upgraded my computer last week. Moved my existing OS install on its hard drive (one of only three components to move....the hd, video card, and an optical drive were the three components to make the move) and fired it up.
What it was......Asus nForce 4 A8N-SLI Deluxe motherboard with 2 x 1GB Corsair XMS PC3200 RAM, Athlon 64 4000+ cpu.
What it became.....Intel 975BX2 motherboard with 2 x 1GB Buffalo Firestix DDR2-800 RAM, Intel e6600 cpu.
The move went flawlessly. Fired right up, not a single problem. On initial boot, couldn't find the proper chipset drivers, obviously, but still ran and ran well. Installed the 975 chipset driver CD and off it went.
Did have to reactivate, but it'd been a while since it last had to be activated, so did it over the 'net without a hitch.
Using this same sequence on moving from various nForce chipset motherboards was always much more drama.
In your case, just dropping in a dual-core cpu in place of a single core should be cake!