Toyota Camry '94 (very good condition prior to accident...only a small, persistent oil leak)

I was recently in a car accident. There was damage to the front bumper, the radiator, the AC fan, the hood, and the passenger side lights. The work done on the car seems well done. However, my car did not start this afternoon. I turned it off last night at 11:00pm and attempted to start at 2:00pm today. There is a small chance the door was left ajar and the dome light remained on draining the battery. I have given the car a boost, but it will not turn over and there is odd, unfamiliar behavior. The electrical system seems to be charged and the car will light up the door ajar light and the ignigition key guide and all inside lights, move the mirrors, move the windows, etc. But, the door needs to be open and the foot off the brake. Also, turning on the lights or attempting to turn on the ignition fully will kill it. I can then reset to the electrical running position with the door open. What should I do? Is the problem with the starter or engine? My gas tank is also low, but this seems extraneous since the car doesn't get far enough in the starting process. This is a new problem. I believe the battery is charged now, as well. What is your suggestion for further action?

Optional Information:
1994 Toyota Camry 4 cylinder

Already Tried:
Boosted battery for 30 minutes; car did not start. Checked fuses, but not in detail.