So, yesterday, I got the 30-day free trial of foundations. When I installed it, I was really hyper because A: It was during my sister's grad party, lots-a-choc, and B: I wouldn't need to go on XFire to get my models exported as a mesh. But, when I installed it, it didn't install. There was a folder for it in C:\Softimage, with the XSI logo in it, but I clicked on the logo and it was just that. A logo. It opened up The GIMP. What's wrong?

What do you mean "installed but not installed"?
Do you have Vista?
Go to Start>All Programs>Softimage Products>Softimage XSI 5.11 Foundation>and click on "XSI Foundation" to see if it starts.
If you don't have this path then you did something wrong.

XSI starts from a .bat

EG:
C:\Softimage\XSI_<version>_Foundation\Application\bin\xsi.bat

I have vista in my house, but I'm not allowed to use it. By installed but not installed, I meant I installed it but I couldn't find the actual program.

Since you aren't allowed to use Vista in your home, i'm guessing you're on XP, so just follow the path that I posted and it should launch, but there should be a shortcut on your desktop or maybe not, it's been a while since I first installed.
Go here to launch XSI if no shortcut exist:
Start>All Programs>Softimage Products>Softimage XSI 5.11 Foundation>XSI Foundation

To make a shortcut on your desktop just right click on "XSI Foundation" in the path shown above and:
Send To>Desktop (Create shortcut)
Then you can easily launch XSI if indeed it is installed correctly.