The timing belt on my 2005 Accent broke. I got the head off and found 4 bent valves. I replaced the head gasket and got a head from a 2001 Accent, the wrecking yard said they are the same. It went on with no problems. The timing marks are aligned per hyundai's service site. All of the bolts are to torque. The engine starts immediately and runs smoothly for a few minutes. As the engine heats up it starts running rough. Then I start getting a pinging noise coming from inside the engine somewhere I can't localize. Once the engine gets hot enough for the cooling fan to come on it wont idle. Once it dies, the engine won't turn over, like if the battery is dead, until it sits for 5 minutes and cools. Then it starts but still runs rough. If the engine cools completely all the above repeats itself. The service engine light doesn't come on except for the self test. Engine compression is 120 PSI in all 4 cylinders. The timing mark is extremely erratic at hot idle. But increasing the RPM above 1000 steadys it but is below scale before TDC.
Does anyone have any idea what this could be? I have removed and rechecked everything, it looks like it should work.

 

Which cam sensor did you use? The one in the junk head or the one from your original head? 120 PSI doesn't sound right, should be 170 shouldn't it?

All that said, it could be a bottom end problem, as the timing belt broke, and you don't know what else damage could have been done.