UCI and UCSD limited numbers of admissions this last year. It made the news. Not sure about UCSB, but most likely guessing that your SAT scores were a bit low for them.
Good news is that as a transfer student, they won't look at SAT scores. At all.
If you were to reapply to any of those schools as a transfer (you will have to wait till 60 units for the UC schools), make sure you follow the IGETC program. Here is the link:
University of California - Admissions
What programs were you applying to for LMU and Chapman?