I'm confused... You said you resoldered it, and it fixed it, but then you said it still has the problems... If it is still having the boot problem, then you need to resolder the max 1987 chip. If it worked for a few minutes, then it was fixed, and then broke again...
did you oil your hinges?
Your best bet is to remove the monitor, and oil the hinges, and then move them around a ton until they start moving easier.
Then resolder the chip. You have to make sure the tip of your soldering iron is super small, if it is too big, you run the risk of connecting pins to each other, effectively ruining your work, and causing the same problem...
I used a magnifying glass when I did mine, and you only have to touch the pin for a second for the solder to flow. If you touch it too long, you can fry the chip, or cause more issues, (connecting surrounding pins, ect).
You also want a low wattage iron. Like a 15 watt.
Resoldering the max 1987 chip is the fix for the boot problems on these laptops. It is caused by the hinge on the screen that gets tight, and flexes the board until it starts to break the chip free...