Could be a waste of money if the battery has been out for a long time the charging circuit is very likely to be no good, as said earlier at least check that there is power coming from the battery terminals before wasting your money on a new battery. 

Is there an easy way of doing this without using some kind of meter (which I don't have) ?

So have you changed the battery yet then?

Is there an easy way of doing this without using some kind of meter (which I don't have) ?

Not really, a multimeter wont tell you the full story as ideally it should be tested under load. Another easy way to tell if its beyond repair is to look on the rear of the PCB (You have to remove it from the case ) there is a large resistor, if that is scorched its most likely too late to change the battery, if its burnt or crumbles in your hand its way too late.

 

Be careful there is mains electricity in the panel

So have you changed the battery yet then?

Need to look in the cabinet first, not that I'll know what i'm looking at.

Will probably buy a new battery anyway, after the stick I got off my missus at 3 a.m. this morning when the fu##er went off !