Ok so this is strange?

I just bought an 06 grand marquis and a couple of times over the last week its been acting funny, One day I had to leave my hazards on for about 45 min and when I went to start the car it started hard, Then for no reason the car started dinging after driving for about a block but no service lights came on. I shut the car off and restarted it and it was fine. Now today after the car had sat for a couple of days the same issue of hard starting, But this time the rpm meter took a minute to come to life and the fasten seat belt light stayed on after I buckled up. After I drove about a block the rpm meter finally came on but then the dinging started and continued for a couple more blocks before finally stopping. I'm going crazy with this, I thought maybe it's the battery, but would that confuse the instrument Panel and same thing with thinking it may be the starter. Computer maybe ? I don't know, Any help you could give would be fantastic thanks, Oh and the car only has 50000 miles if that helps.