Sounds to me like the power shutdown / GPL:installation doesn't have anything to do with it, since it was already slow after a reboot. Leaving your pc always on isn't a smart option either. Could be a lot of causes for the peformance problem: high temperatures, faulty drivers, correptud OS, virus, defect gpu, memory leak, bad hard drive etc.
If I were you I would make a sort of checklist to rule all the possibilities out to find the cause:
An easy start would be to use a program like Malwarebytes and your anti-virus program to do a complete scan of your system. Also after a reboot, you should open the task manager to see if cpu/memory activity show unusual behavior. You can use S.M.A.R.T. to see how healthy your hard drive is.
There are also multiple programs to check your cpu and gpu temps, if they are too high they will throttle down and peform worse. And since you say the problem goes away after the pc is in on for a long time (idle?) high temperatures could very well be the cause.
Edited by Millennium, Jan 24 2018 - 01:30 PM.