If you only have 3MB of space left on C: I'm thinking you are going to be having way more problems than just trying to install SQL server.
A. J. points out the issue with installing SQL is that no matter what you do there will always be some files install on C: This is true of All MS applications and most others in the windows world.
Add to that the fact that there are certain log files generated in C:\windows\system32\logfiles that various applciations use and update. If you only have 3 MB of space left, you're going to have an unresponsive system in VERY short order. Once you reboot you'll probably get a little space back as your page file is decreased, but you need to address the C:\ drive before you do anything else.
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