When you have the "!(o)" icon shown in the notification (out of phone internal memory), then it would even complain text messages full, although theoretically phone internal memory should have nothing to do with SMS.Even you delete all the SMS threads, you would still not able to receive any if you don't have enough phone storage. (note: Liquid only has 200 mb internal).
If you have make enough room on the phone internal storage, you should be able to receive SMS again. I needed to keep at least 20 MB free on my phone to keep the icon from showing.Once it dipped below 20, i would have tons of problem.
However, I don't know voice mail would be impacted as well.
Try going to settings, applications, manage apps, browser, clear cache
I've found that browser's cache needs to be cleared every once and a while, and seen it as large as 70mb... when theres only 200mb to start with, that's a huge chunk of it.