Lights and battery should have no impact. Depending how hard it was forced into neutral might be a contributing factor in that the shift leaver is not making the proper contact.
However, I am suspecting your bigger problem is that you possibly ran the car too long while the fluid level was too low or that you have a fluid leak that you have not detected. I am not a mechanic. The car is 15 years old. I do not think you want to put a lot of money into it. You can have it towed (by a tow truck, not pulled behind another car) and get an estimate. I think you are going to find it expensive.