I think I am safe in saying that it is perfectly Ok to use it without the battery and run it solely on the mains adaptor.
I guess it was second hand?
If so the battery is probably dead. It may have reached the end of it's life, as rechargeable batteries have a finite charge-discharge cycle, OR it may have been 'missused' by the previous owner.
But in either case, you should be able to run it off the mains without the battery.