Q: How to get a 2010 MBP to start up

So I have a mid-2010 unibody 15" macbook pro.

For the last two years it has just sat on a shelf, dead because something has failed and the screen goes black during boot. Sometimes this completely shuts down and restarts the machine, but sometimes it doesn't and the computer continues to boot with a black screen.

SOMETIMES if I wait a week or so, I can make it all the way through login before the screen goes black. Most of the time it goes black doing boot and doesn't make it to the login screen. The longer I go between trying to start it, the longer (usually) the screen will stay on before going black. After the first time, though, repeated attempts to start the machine will always give me a black screen within 10 seconds of startup. Research shows it is probably the discrete graphics card or the logic board itself.

I used to be able to wait a while, then use the keyboard to log in with the black screen, then use another computer to bluetooth screen share and operate the laptop that way. An external monitor does not work, but screen sharing used to. It doesn't anymore - not sure why. Perhaps the bluetooth has failed, perhaps it is no longer making it all the way through the boot process to the login screen...I cannot tell. When I press the caps lock button, the light does turn on, so something is obviously happening but I have no idea if I am logging in when I type in my password...I don't hear any increased activity in the computer itself, it sounds dead silent.

It seems a lot of people have been able to get their MacBooks to work by using some program to disable the discrete graphics card. I would like to try this, but I can't get the computer to stay on long enough to get this program on it and switch the graphics card over. I have tried booting in single user mode, but the screen still goes black. Tried booting to Recovery mode but the screen still goes black. I thought to try installing a fresh OS but I can't make it through the install process before the computer dies.

So, if anyone has actually read through this novel, I guess my question is - does anyone have any idea how to get this thing to boot up, in any way or form? Can I take the laptop apart and manually disconnect the discrete graphics card? Is there any startup mode that uses only internal graphics? I have read that if you overheat the laptop and then restart it, it should let you on long enough to disable the graphics card, but my problem is my laptop does not stay running long enough to overheat.

Searching for desperate options out there, anything and everything. I don't want to put any money into this old dead machine, but I would like to get it running again if possible.