I know--I should look for a part time job more seriously than I have been, but fewer jobs hire with no experience here than you seem to think. The last 5 jobs I've considered as a cashier required 2 years of prior experience. I really don't care about glamorous at this point, and I guess I should mention that lack of transportation is the most limiting factor.
There are plenty of jobs that don't need experience. Some jobs I did while going to college:
Grocery store: stocker, bagger, the deli, the fish dept, etc. No experience needed. They teach you to cashier if you want to learn. they work with students ALL THE TIME and accomodate schedules easily. Look at Sam's club, walmart, fred meyer, safeway, krogers'. My brother worked in the men's dept at Nordstroms. Dressed nice, made lots of money, met lots of women. Seriously
Pizza Delivery: you said you don't have a car. Borrow one. Deliver pizzas. I was making $50/night in tips alone, more on the weekends.
Wait tables somewhere, anywhere. If you give great service you will get great tips. Ride your bike, take the bus.
The library: if you know your alphabet you can shelve books. I worked my way through college in the library. It's open all night too and you can study while you sit there waiting for folks to check out their books. You can listen to your ipod (with your classes or review material on it) while you shelve books.
Get a CNA license or a phlebotomist's job and work at the hospital. they are all about folks going on for more higher education. they will work with you with your school schedule.
In the summer I worked double shifts at the store and the library then delivered pizzas on the weekend. I also worked some in the tourist business serving coffee and talking about local stuff to do.