I tried to send a couple of MMS messages and they remain in my outbox with a clock symbol next to them (as opposed to the sent/check symbol). In the meantime, I have sent and received SMS messages but I have also been unable to receive other MMS messages. I've turned the phone off and back on again but that did not help. Any suggestions?

Sounds like your data connection is failing. Are you able to open and interact with a webpage?
Do a battery pull (with the phone turned ON).
If it still fails, do a register now:
go to options, advanced options, host routing table, hit the menu key, choose register now.