Can someone help me figure out what's wrong with my computer?

Every day I get computer updates. For this one, it seemed to have removed most of the links from my desktop and are replaced with those little white pieces of papers with the corner folded. When I try to click on them, they don't work. It seems as if the links to open the programs are in "hiding", meaning they're there, but I don't know exactly where they are.

However, I've figured out that if I right-click into properties and highlight the "target" link, I can open up most programs. For some programs (Like the Sims) it doesn't work for some reason (I have Deluxe, Seasons, and got University Collection for Christmas). So I tried to uninstall all the games but the computer says they're uninstalled, but it has left behind pieces of the game that make them still installed.

Sorry that this turned into a two-part question, but, can someone at least help me with the first problem?