Boot loops (black scr) for long time (20 min - hours) before success

I have an early 2011 MacBook Pro 15”, with the following set of symptoms :

On battery, if I press the power on button, I can hear the fans and disk come to life, but there is nothing on the screen, and it the disk powers down again in a few seconds, and then nothing happens. I need to press the power button again to make the machine attempt another start.

On AC power, the behaviour is similar, but the hard disk takes much longer to power down. (I need to stick my ear pretty close to hear this). However, it attempts to power up again by itself immediately. (Disk spins up, IR light on the front blinks). This keeps happening, the screen is black, the faintest switching off of the backlight can be seen on each loop, and takes anywhere from 20 minutes to a couple of hours, when the machine finally lights up. The duration of the attempted restart cycle gets shorter and shorter. After this it boots into the OS and works just fine, and both the integrated graphics and an external display with the AMD graphics turned on run fine as well. Shutting down and restarting works correctly after this, until I leave the machine turned off for a while, after which the same problem occurs again.

I have checked the disk for errors, reset the SMC, and reset NVRAM, but the issue still remains.

The battery maintains its charge and works as expected - it has been replaced recently.

This is a pretty unusual set of symptoms, I have not been able to find any other instances of this discussed online.

Any insights / suggestions as to what this problem could be, or potential solutions would be greatly appreciated.