After unhooking and then hooking back up my battery, my check engine and VSC lights came on. Also now can't open my trunk or fuel filler door from inside car.

when check engine light comes on VSC is disabled. small leak is for evaporative system (to prevent fuel vapors from entering the atmosphere) small leak is A leak less than forty thousandths of an inch, it could possibly be a gas cap not fully tightened,leak in a vapor line,leaking fuel filler neck,gas tank leak,purge valve,vent valve just to name afew. clearing code will turn off both lights but if theres a leak lights will come back on.

check all your fuses in engine compartment and under dashboard engine check light comes on every 3000 miles for oil change reminder

There is a fuel filler door release switch on the driver's side door in the map pocket. The fuel filler door will pop open when the switch is pressed. It is closed manually.

If this system is malfunctioning, a manual release is located in the trunk. Remove the access cover which is located on the left-side inner trim panel and pull the release cable. The fuel filler door will pop open.

Source: Owner's Manual pages 418-421

Dodge Charger Owners Manual

OK try this: make sure the fuel filler cap is on tight. Toyota (and Lexus) checks the EVAP system for leaks and if it finds a fault it lights the CEL and VSC. If the fuel cap is loose or the rubber seal on it is cracked then this will be seen as EVAP leak. To clear the CEL etc disconnect the battery negative terminal for five minutes (you may have to enter the radio security code after this so have it available when you reconnect the battery).

Pull the trunk wall lining back by the fuel filler. On my 99 A4 there is a red cable there - it's an emergency release that will pop the gas door open.

Yea VSC lite will come on when ever a check engine lite is On, the codes you mentioned are certainly a EVAP codes, make sure your gas cap is a factory and inspect seal surface and contac surface on filler neck for rust clean if any,also check all hoses going into air box reconect if necesary, (have your car been in any accident) if have access to a scan tool resest lite if lite comes back no other option take it to a dealer, check for warranty coverage on this systems.
good luck

There should be a cable in the trunk for a emergency release

Most cars have an emergency fuel filler door release somwhere in the trunk. Look for some kind of pull cord close to the area of the outside fill door.

well for starters there is many factors at play here. 1. battery chargers need to be on and battery disconnected. make sure if it has a timer it did not run out and (the charger may also have an internal fues/ relay ) if it gets too hot it shut off. Was the charger on a high enough setting to compenstate for the drain and is your battery good enough to be charged even. constantly drained batteries will actully not hold a charge after awhile. most parts or even walmart can check batteries free>
The trunk lights and fuel door on the same fuse? otherwise I would say the trunk has a bad switch that is not making contact or is making poor contact and acting as the trunk is open. it may just be pinched wires that rubbed together make contact with your cars steel body. They may be seen in the trunk follow the wires from the release switch and see if it connects anyplace near the fuel door. I am sure it will.

Please note that when the engine ECU sees a problem, all 3 of those lights come on at once. What you need to do is have someone put a scan tool on your car and check the DTC code(s). More often than not, a loose, faulty or aftermarket fuel filler cap will def set the light on.