Your "ancient" machine is newer than anything in my shop, including the computers used to design, program and test these miners. The only processor of comparable age, I think, is in the hosting router which handles 22 firewalled VLANs with independent VPNs through a rebuilt gigabit managed switch.
As a third-generation Broke Person it's always hilarious to me what people consider obsolete. Your machine should be sufficient, with appropriate hubs, to run a dozen or two R606 no problem.
Handy that the PSU is enough for both.