Hi
Is it a 1108cc engine or an 899cc? The reason I ask is that the two engines are of quite different designs and I only have experience of the 1108cc FIRE engine.
Assuming you have the 1.1, and they haven't changed the engine from that of the cinq and the uno, the starter motor is behind the engine (side nearest the dashboard) as you look at the car from the front. I would suggest a few things
1. If you turn the key and the starter dosen't try and turn at all then try feeling for the two electrical connecters that go to the starter motor. On my uno the earth connection was faulty and this is an easy fix as i just cleaned the connector and put it back on and it worked
2. If it is the motor itself that sounds as if it is dying it is very easy to replace. I payed about £10 for a replacement motor from ebay and I can't see a scrapyard would charge any more. To replace there are three bolts that need to come out. The only problem is access is a little akward. Pop the new motor back in, cross your fingers that it works and your away!
You may be able to service your existing motor (replace brushes ets) but i didn't even investigate this as I could get a new motor very cheaply.
Hope this helps
Phil