Use the following logic to troubleshoot (a cut & paste from what I sometimes send people):
Control from the PID to the heating element goes like this:
PID -> SSR -> ELEMENT SELECT SWITCH -> RELAY (BOIL or HLT) -> ELEMENT
(note: You may not have the element select switch or the relay)
While the below deals with the element not coming on, the logic holds true of the element is always on too (just do the reverse):
When the PID is sending a signal to turn on the element, the PID "OUT" light should be on. If it isn't on and you expect it to be, stop there and look in the PID for the problem. The settings may be incorrect, the temperature may be set too low, or you may be using it incorrectly.
If the PID "OUT" light is on then the SSR should be receiving a signal and turning on too. If the SSR light isn't on (assuming there is one) then there's an issue either in the PID output connector (PID is defective), in the wiring between the PID and the SSR (check your wiring), or the SSR is defective. To troubleshoot a possibly defective PID or SSR, swap it with another PID or SSR.
If the SSR light is on but there's no heat at the element, then either the relay between the SSR and the element isn't closed, or there's a problem with the element, or the wiring between the SSR -> ELEMENT SELECT SWITCH / RELAY -> ELEMENT is incorrect, or the ELEMENT SELECT SWITCH or relay is defective. It is also possible that the element itself is defective. Switching the ELEMENT SELECT SWITCH to either on position should make the corresponding RELAY close with an audible 'clunk' - if it doesn't check your ELEMENT SELECT SWITCH wiring.
Using a voltmeter to measure for 240V at the various points along the chain can help troubleshoot the issue.
Refer to the owners manuals of the individual parts for further troubleshooting. The PID manuals are especially useful as they contain further troubleshooting tips.
Good luck!
Kal