That is the messed up thing about this industry. Every job requires experience (even the most entry level position), but no one will give you a job without that experience. So how in the world do you get that experience that no one will allow you to obtain!?!?!
I ran into the same thing, and i'm sure most others have to when they were first starting out. REally your best bet is to have a degree or certifications. Those are the 'stepping stool' that will allow an employer to look past your lack of experience and give you a shot. They'll see that maybe you don't have any experience, but you must know something if you have a computer degree or a few certifications.
A computer degree of some type is the most valuable (CIS / CSC), but certifications can be an option if you can't get a degree. I would personally start out with A+ and Net+, then an operating s ystem certification like Windows 7.