2000 Other Fiat Models Punto Wont start

First check battery voltage with a volt meter, a fully charged battery should read about 12.6/12.7v, if less than 12v your battery is discharged and needs fully charged up, or if it does'nt hold a charge, replaced.
Check the earth connections from your battery and make sure the connections are clean and tight.
If your engine still fails to turn over then you may have to check the starter circuit i.E. Fuses, relay, starter solonoid, starter motor, ignition switch and associated wiring for broken or loose connections etc.
Good luck.