Sounds like a bad earth to the starter or a weak battery.
If I remember rightly to check for the former, connect a jump lead from the NEGATIVE battery pole to the starter motor body and try again - if it works then it's the earth on the starter.
The starter motor is on the back of the engine below and in front of the air box.
- Undo the jubiliee clip holding the air intake pipe on at the front of the engine bay and pull the pipe out of the concertina bit.
- Undo the jubilee around the top of the carb body
- Unclip the spring clips on either side of the air box lid
- Twist the airbox lid anticlockwise to unclip it
- Lift the airbox (and the flat oval box that connects it to the carb) upwards (you'll probably need to unclip the guide that's holding the fuel line to the plastic intake and disconnect the breather pipes from the flat oval box).
With all the air intake stuff (and box) out of the way, you should be able to reach the starter by leaning over the engine either from the front or from the side (passenger side is easiest assuming UK car) depending on how tall you are.
This is by far the easiest way of getting at the starter (rather than putting it up on ramps and scrabbling around underneath).
The starter is held on with 3 long bolts and the earth is held on to the end of it by a nut.
Removing the above will take 5 minutes and when I changed my starter that only took another 20, then 5 minutes to put all the gubbins back on again.
If your starter is buggered completely, don't expect to pay more than 25 quid for a replacement (recon) - It is the same starter as the Citroen AX-GT too (same engine).
Cheers, Matt