Your prints aren't too dark. Your prints are what they are. The job of monitor calibration is to make the screen match the prints.
No chance at all, I promise.
Then it's time for a new screen. Let's not waste any more time on this.
However, when I say "new" I don't actually mean new. https://www.facebook.com/groups/195567190503489/permalink/2659777307415786/
It really sounds like graphics card interference in your new computer, doesn't it? I can't think of any other explanation.
Maybe see if it's possible to temporarily turn off the graphics card?