Normaly, you don't need to have the battery in place to use on the charger.
If it only get power with both the charger AND the battery, you have some hardware fault.
That fault may have caused the battery to overheat.
The overheating battery may have caused some more damage.
Have both the old and new batteries checked to make sure that they are OK.
Have a technician check your computer for any damage.
Fixing the computer can be very costly if the faulty component(s) are hard to find or welded in place.
It may be cheaper to get a new computer.
A new computer will be more performant than your actual one.
Electro
September 2014