If the old PC is compatible with the new one, you could swap out the PSUs. But be sure it isn't an old Dell from the P4 era. They had proprietary PSUs/MB 24 pin headers back then.
You could also pick up one of these and test the PSU. But it will simply tell you if the voltages are correct:
http://www.amazon.com/Rosewill-Digital-Supply-Tester-RTK-PST/dp/B004Q7FUGM/ref=pd_sxp_grid_i_1_0
You could do the same thing with a VOM meter, a schematic, and a paper clip.