Urgent! I485-dependent EAD expired and stuck. Can I apply for H1

Dear Gurus, My EAD renewal is currently stuck in Texas Service Center even though I applied 100 days before my expiration date (Receipt date: 03/28/08). I have been out of job for two weeks. I have called USCIS many times, but not sure it will be resolved soon. Can I ask my university to apply for an H1b for me? Thank very much for your suggestion.