check out the answers to this question: http://questionland.com/questions/8226-do-dental-schools-do-discounted-wisdom-teeth-procedures

You should try calling the UW dental school first, but if they want a referral try going to the Central Area Dental Clinic. It's at 2101 E. Yesler Way, phone number 206-461-7801. That's where I went when I was in the same situation a few years ago; I had to go early 2 days in a row to wait for an emergency appointment. (Get there before 7am for the best chance to get in.)

They couldn't help me with my broken tooth, but referred me to the UW dental school for a root canal. The dental school turned me down because my molar roots are too complicated, so I put a root canal on my credit card. Then I fucked up and didn't get the crown on right away, and my tooth decayed beyond help. I should have listened to my dad and just got it pulled before dumping all that money into a borderline salvageable tooth. If your broken tooth is a molar, you might want to think about whether it's worth $1500 to save or whether you should just have it pulled and save for an implant in the future.

If you can get accepted as a regular patient at the Central Area clinic you should do that - it's pretty cheap and although it's not the best dental care, it's better than nothing. I got some fillings done there that really helped.

Finally, getting knocked out is expensive and I'm not even sure they offer it at sliding scale places - they might be more sympathetic if you say you are really, really scared of the dentist. But even with my dental insurance I had to pay quite a bit to get laughing gas when I got the remnants of my broken tooth pulled out by the oral surgeon.