2005 Saturn Vue Radio/Low Battery?

Radio got wet in storm. Would not work at all after 8 months bought a new radio from Saturn dealer and had them install (March 2010). 2 times after that my radio reset to 12:00 and I lost all my preset radio stations. Took it to the dealer - told me it was my battery - that my car was 5 years old and due for a new battery. They started the car w/ no problems a few times but still insisted it was battery or they would charge me $46 to look the problem. I have had no problems whatsoever with any other system (lights, horn, locks, etc.). 8/15/10 started car, I put radio on, had CD in. Took a minute to get going (thought it might be due to extreme heat we have been getting). Later that day turned radio on and it did not turn on at all. Today noticed the time was different then yesterday (stopped at 10:37 yesterday and was 11:00 when I turned on today). I turned radio on and it worked. Turned it off to reset clock and then turned radio back on but it did not work. Want to have my ducks in a row before I go to dealer. Could a low battery cause these problems? Also, I assume if electrical or a fuse that would have been checked when they installed the new radio. Your thoughts please.