continuous beep right away after moving switch on throttle to run

I have a really annoying beep that will only go away if were feeling lucky or when we cruise around for about 2 minutes. The beep comes on right when we turn the switch to run. It will do it when the engine is completely cool, and hasnt been driven. My first couple of guesses were the depth finder's transducer was acting up or it was a low battery warning. The reason I thought it was a low battery was because it will turn off after cruising for about 2 minutes, I was thinking the battery was getting charged by the engine at that point. It wouldnt beep at all during the day after we had ran the engine for a bit, but the next morning we would turn it to run and it would beep again. I have read online about these impleller lines being clogged and the pisser not poring out water but my beep comes when the engine is cool and plenty of water is coming out of the pisser. Were going to get a new battery to see if that solves it but Im just not so sure it will do the trick. I also had another issue with my trim not wanting to raise up or down and once we wiggled the connection on the battery then it had no problem. I think its a battery issue but wanted to get more opinions.

I have no owners manual its a 2005 milan (hard to find manuals for them because they no longer make the boat) the engine is a 5.0L Mpi mercruiser.

Thanks for the help!