i know of many that had exchanged a TK-56 to a TL-60 with no issue. These were done on a hp dv94xx machines. A straightforward removal/swap of the cpu with new thermal paste.
From a TK-36 to TL-60 is quite a jump, but doable, I guess. Have u tried looking under ur bios settings after installing the new cpu and see if anything is out of whack? Is there a bios update version available? Faulty cpu, as u mentioned, could be a reason.
MichelleG probably has an idea, just wait for her input & response
cheers ...