Some times it runs for long periods of time but then when I try to work on it well it shuts down, or the screen goes...

I installed a 1 TB hybrid drive in my 2009 27" iMac, the reason I did this was so I could remove the sensor off the old 1 TB drive and put it on the new hybrid drive (SSHD). That way the temp sensor does not run the fans at super full speed. Also at the time I read about SSD's they need to be purged once in a while, maybe not now but 3 years ago I think that was the case. So with the hybrid drive as it needs to it can purge the caching flash part of the drive. In the end the programs and files I use all the time are right there and the stuff I don't use all the time is still in the deeper storage on the HD side, so it starts up quick and programs I use all the time open right up. This seems to work well for me. I have a 2 TB drive on the time machine that I only turn on once in a while.

Just use another monitor till you buy a new computer, I have my macs all hooked up to large screen tv 45 inch or better. I can sit back and work, with a wireless keyboard and mouse I can sit in a good chair and use a coffee table.

I had this issue with a recent job, replaced the power supply, but the connector to the logic board was not connected all the way in. So i got it all put back together and then had to take it apart again to reconnect that plug. Then it worked fine but I still have an issue with the screen. The user has it on full brightness all the time which is not normal, I think that may have caused an issue with the power supply, and the left side is darker now and I have seen all kinds of fixes for that, however I think the backlight is just bad. Good Luck.

I did kinda the same thing when I replaced the mother board, the heat sensor for the Graphics card broke into pieces when trying to unplug from the old mother board, ah ha, there was another connector to the heat sensor for the cpu I think, so I clip it off, and soldered the new connection but forgot which wire went where so when it was all back together the hydro cooling fan spun at high speed because the machine was not getting feedback, so I took everything apart again and switched the wires and plug them in (the connector only goes in one way), not its all working like normal all 4 leds are on it must be ok. I did have one of the ram chips go bad in this mac even though the system report said it was good. Its a 2008 24 inch Running El Capitan with no problems and only one 4GBs of ram. So I am pretty happy.

do not use a vacuum cleaner, it has ESD!!!!!

find a vacuum that is for computer use that has no ESD