My daughter has a 1.2 Punto of 2006 vintage. This may not be related but I'd best mention it just in case, because her car had all sorts of odd electrical faults and management warning lights until I found it!
The main earth cable goes from the battery negative to the gearbox, just under the slave cylinder, but it has a tag crimped on to it half way down its length, which goes to a stud on the chassis leg to act as a body earth. Despite looking absolutely perfect, the cable had corroded to almost nothing INSIDE the heat shrink insulation where the body tag was crimped on to it. I just gave it the tiniest tug and it came apart! After I'd replaced the bottom half of it with a generic earth strap from my local Halfords, it was a different car!
Also, while I remember, the main fuse box lid (on her car it's against the left hand front wing near the bonnet hinge) is difficult to fit properly (the bonnet release cable gets in the way). If not fitted correctly water gets in and causes all sorts of electrical havoc. That said, I think the 2002 model might be different?
Last thing (again, not sure of your car will have one) but my daughter's has two lambda sensors and the bottom one was loose in its fitting.
Good and friendly Punto forum here:
http://www.fiatforum.com/punto-ii/