IMHO, the easyest way to figure out if the CPU is overclocked is to use WCPUID and compare the data with a reliable online source ( Sorry, I can't give any links at the moment ).
Figuring out if the CPU is dead is even easyer, the computer won't POST after being powered on.
Finding if the CPU is reliable is trickyer, your best bet would be to run a distributed computing software ( seti@home and the like ) for a few hours and see if the CPU overheat ( using a CPU monitoring software ) or crash.
Before you do any of the following, check if your motherboard and BIOS will support this new CPU, if not, flash your BIOS with the appropriate version from your BIOS manufacturer.
If you can, run those softwares before you open your wallet, a one day warranty is suspicious.