Chosen Solution
I don’t know if you were able to fix the display issue or not but I ran into a similar problem as you with only 3 LEDs lighting up on boot, after I upgraded the processor, airport extreme card and swapped the HDD for an SSD. I also thought that I might have broken the LCD connectors or might have done something to damage the logic board but that did not turn out to be the issue. It felt strange having a damaged logic board GPU or LCD just by taking it apart. Anyways, the fix that worked for me was reseating the GPU. So I basically took the whole thing apart again and took off the GPU by removing its heatsink and then added fresh thermal paste. Although I hadn’t touched the GPU earlier I had a feeling that this had to be the culprit (Maybe it had come loose or something). I then put everything back together making sure that the screws were properly tightened and It powered right back on with the 4th LED lighting up and Chime. So basically I went from first 3 Solid LEDs, no Chime, spinning fans, black display to 4 Solid LEDs, Chime, fans spinning and display powering on. The machine is working fine now. My iMac model is mid-2007 20". I hope this helps! Other fixes I tried that didn’t work: Resetting the SMBResetting the PRAMReplacing the batteryFidgeting with the display connector / Inverter cables on the LCDTaking off the LCD ribbon cable and reattaching itReconnecting the original HDD and Wireless/BT cards
No - TimeMachine is restore-ware, not a boot able clone. What do the LED diagnostics tell you? Have you tried to boot the good HD using an external monitor? If this answer is acceptable please remember to return and mark it.