Hi, I've got the same laptop and had similar issues. Haven't upgraded to 8.1 due to some bizarre recurrent updating issues I'm working through currently, but the most consistent fix I've found is simply playing windowed. If a game has the option, launch borderless windowed fullscreen, but as most games don't yet have that option, you can launch the games at 1080p windowed, then use a program like fullscreenizer (or equivalent) to remove the windowed border and automatically move the co-ords to 0,0 so it's indistinguishable from fullscreen. Also, if it's a poor console port and doesn't even have an option for windowed, you can use a program like Dxwnd (or again, equivalent), to force the game to run windowed and then do the whole fullscreenizer thing after that.
Alternatively, you can try the enduro fix Drivers. There used to be a link
here, but it's since been taken down, and I can't find another link so the windowed fix is the only viable one thusfar it seems.
Anyway, hope that helps, and if you haven't already, make sure you've got the latest 8.1 drivers for the 3540 from
here.