Car not starting correctly

My car was working just fine yesterday, though the service vehicle soon light had come on.  It appeared to be the front left headlight had gone out.  Wasn't able to take it to be fixed quite yet though, I was going to do that next week and just drive only during the day for now.

Now today I try to head out to the grocery store and the car won't unlock.  I thought it was just my remote died since the car is old and all, so I manually unlocked it with the key.  Tried to start the car and the service vehicle soon light came on along with security, and one that looked like battery and oil.  It did start, the lights came on inside, the radio was working, but the car wouldn't move.  Since the only electrical thing not working was the locks (and likely window), I'm doubting the battery went out entirely, car doesn't start at all when that happens and I just replaced it less than a year ago.

I stopped it, waited about 30 seconds, tried again, same thing.  It appears to start fine, but all those lights come on and it doesn't go anywhere.  I just want to know what is wrong and how to fix it or how much it will likely cost to get someone else to do it.