from the SiS chip I am guessing you have integrated graphics, that could be causing your issues.
Another thing that could be causing issues is the lack of RAM (256MB is a tad low, 512MB is standard), I am not saying the RAM is making it say "No 3D controller" I am saying the RAM could be another thing affecting your game's performance. The SiS website may have most of the answers you need. Another idea would be to goto the computer manufacturers website or where you bought the computer. I would just check the SiS website, if you have trouble finding it, just goto Google and type in SiS.
Also what games?
You may solve the problem by contacting the people who made the game.
Are there any other performance issues, and what caused it to start dropping games? (It seems like you had the games playing correctly and then they stopped, what did you change, such as a BIOS change or something in the Graphics Settings, you may have a graphics setting too high for your chip)
Also you may be under the requirements of the game with that chip, I don't know SiS chips that well, but that chip may just be too weak to play some games (for example if you are trying FarCry or Halo it's a strong possibilty since most value cards have issues with those titles)
Well hope this helps, but my #1 suggestion is to contact the computer maker/SiS/game maker
contact those 3 and see if there are updates/drivers/patches that kind of thing.