Welcome Ian,
My first question would be, what condition the battery is in.
A battery can show a full charge, but when an electrical load is placed on it, it fails quite quickly if it isn't in good shape.
If you have a battery that you can remove the caps on each cell, check the fluid for it's specific gravity with a hydrometer, a fully charged battery should have a specific gravity around 1.26, if my memory is correct .
If you have a sealed battery, connect a voltmeter to the battery terminals, then crank the engine over with the starter, a good battery and starter would show no lower than 10.5 volts with a fully charged battery.
If the voltage is low, it could either be a battery that needs replacement, or a starter that needs some work (dry bearings causing excess current draw, not leaving an adequate amount to operate the ignition system).
I don't know how mechanically inclined you are, but to remove the starter and dis-assemble it clean and lubricate the bearing and sliding parts surfaces isn't a real difficult job, or if you have a local shop that specializes in starter repair, may be a quicker way to go.
There's a 'sintered' bearing, or bushing at each end of the armature shaft, and they get worn out without lubrication, and my guess is that the starter hasn't been looked at since it was built 27 years ago.