I said Chrome, but I think that's somehow related to amount of memory use.

Last month I could play Worms fine with Google Chrome opened, even with a lot of tabs, but now I can't, when I open the game, all I see is a black screen with a white border square on the middle top.

Skip logo option enabled.
Using Worm kit.

This is the wrong game's forum entirely, but have you tried looking at your palette.log file in the main WA folder? Does it say anything about Chrome in there? If yes, you might have had different websites open in it at different times and only some of them were stealing the game's palette.

Currently the only practical solution to that happening is not having such stuff running in the background, to my knowledge.