Hi,
From what you say the power supply is almost certainly faulty - I would try to get a replacement rather than fix the power supply - PSUs can be dangerous I'm told. An AT (or even ATX) power supply can be adapted relatively easily, just google it.
Also, it's absolutely safe to remove the battery - don't hesitate for a single second that b****r would leak any moment and do nasty, irreperable damage. A pair of pliers are usually good enough for the job, though you could of course try desoldering it for extra caution.
