You're not going to like the answer.
Your laptop is 11 years old. . .it fought like a champ, but components fail. MAYBE. . and this is a *HUGE* maybe there's a cable that's starting to get frayed internally, or the thermal paste has dried up and is causing the GPU to overheat..
More likely the GPU is going. Obviously hard to diagnose from the other end of a screen, but either way the cost to repair is going to be more than the machine is worth unless it is a VERY simple solution.
My best advice is: It's time to put the poor thing to rest and get a new machine...