could i use a C compilier instead of CYGWIN
does it still make eboots?

They're different things.  I believe you're referring to PSP programming eh?

Cygwin is (not exactly) a Linux emulator for Windows (again, it's not really an emulator; can't remember but I think it emulates some POSIX stuff on Windows).
Anyway, that's all Cygwin is - it doesn't compile anything, but it's sometimes required to compile stuff.  It's required to compile up the PSPSDK.  I believe Cygwin has gcc (C++ compiler) included.

Well, taking the technical part out of all of this, you have two choices:
1) Use a precompiled PSPSDK - there's one posted at PSP-Hacks
2) Set up Cygwin and compile the SDK yourself - this is the most popular choice, as it gives the best options, but it's more difficult and not even "possible" on some computers.  Check http://psp-programming.com/ for info on this.

I'm not much into PSP programming, so I can't help much.