my fiat punto cut out and it sounds like its still on?

Has the car engine been overheating? This could make the fan run on.
If not then you may have a faulty radiator thermo-switch. Should be fairly cheap and easy to renew if required.
The fan running may have flattened the battery causing non start.
Unplug the rad. fan temporarily to stop it running .
Check the battery voltage, recharge if necessary.
I would NOT use jump leads to try and start the car, unless you know the correct method they can cause power surges which can damage the electronics of both cars.
If the car has been overheating or will not start with a good battery start a new post giving more details.

tops4589
August 2009