The white LED on the front edge of your MBPro is the sleep light. It will come on briefly at boot, until the display comes on. If the LED remains on, and nothing on the display, then likely the display is not being recognized for whatever reason.
Did you try an SMC reset? or a PRAM reset? (Do both)
If the resets don't help, then try reseating the LVDS cable (that's the large cable (it plugs in at an angle) near the hinge that runs up into the display. Make sure that is seated properly, then try booting to check if the display comes on.
Plug in an external display, to see if there is any video signal to that external display.
But -- you said your video does come on briefly sometimes... It's possible that your overheating issues have damaged some of the chips on the logic board, such as the GPU, or the CPU. You COULD also try re-pasting the heat sync compound, as you do get some response, and maybe it is just heating up very quickly, then shutting off (if it turns on at all)
Are you sure that there was a problem with the fan(s), and you know that the fans were not working at all before you replaced them? Usually, a fan bearing fails, and the fan gets noisy, or maybe won't turn at all. If the fans were working, but making some noise because they were working at full speed -- maybe that was simply the fans working properly, but something was getting very hot (making the fans work overtime), and that issue is still there, and might now be indicating a failure on the logic board, damaged by overheating.