My first guess would be overheating (check the temperature using some tool if you can) but considering the issue with websites you're having (which use quite minimal GPU acceleration), I'd consider trying a fresh install and/or using Ubuntu (don't need to install it - put it on a USB stick and boot from it without installing! Installing will mess up your boot loader!) to check if it might be a windows or driver problem.
Can also narrow it down by plugging your monitor in the motherboard's HDMI port and relying on the Intel (?) internal GPU for a bit.
A 980 is by no means dated. It can still run all games on highest settings. It should not be close to breaking yet. Message me sometimes otherwise for details ... Lots can be done really.
Reminds me, make sure the graphics card is seated firmly, the connectors inside the port are undamaged (same for the cable). Also make sure to check the windows event viewer, can see logs there of any errors.
Note: I realize you said you used watercooling, but watercooling is no magic wand. Its effectiveness depends fully on the setup, distribution of heat in the endgame. Managing a self-built PC takes vigilance, watercooling or no. In fact, Watercooling can perform far worse and end up being extremely expensive to replace if you don't replace your cooling liquid every 6 months or so. Have you checked the liquid lately?