I can't tell from the pics if any of the wires are shorted together, but it's either that, or the internal timer relay is faulty, or the thermostat is shorted. I'm sure that you disconnected the thermostat to see if that was the problem. If you don't need the external relay (and the thermostat,) I'd bypass them. Here's how I'd check the timer and wire it-
0. TURN OFF POWER
1. Remove all of the wires from the back of the timer.
2. Connect Neutral (White) to terminal 1 of timer, Hot(Black) to terminal 2.
3. Check the internal timer relay with an Ohm-meter, should be open (infinite) between terminals 3 and 5 and shorted(very low resistance) between 3 and 4.
4. Turn on power, timer should display time, check for voltage between terminals 1 and 3, 3 and 5 and 3 and 4.
5. Cycle timer ON-OFF, while watching for voltage changes between 3 and 4 and 3 and 5 (IF there was voltage present in step 4, if not check for resistance changes.
If the internal relay is working, then you will see voltage/resistance changes on terminals 3/4/5. if you don't, them the internal(Timer) relay is bad.
If the internal timer is OK, then TURN OFF POWER, connect neutral (White) from line and load to terminal 1, Hot(black) from line to terminals 2 and 3, and Hot(black) to load from terminal 4. Turn on the power, and enjoy!
Good Luck!