Frustrated.

OK, so I am working as a call in contingent employee in a position that I like- but not ideal (weekend nights only 16 hours every 2 weeks & not using my degree)- and i applied through an 'in house' application for a position that just happens to be full time with another department- I got a phone call from HR saying that they WILL NOT send on m application because it is a conflicting schedule with my current position.
Currently I am contemplating quiting- because I cannot get benefits as a 'call-in contingent employee.' I understand that it is hard for them to train and invest in me for me to turn around and quit- but the issue is not that I am only a few months into the position- which i understand if it was for that reason, but that is not the reason. I'm so frustrated!