A quick test - clip a jump lead between battery earth and engine block. If the starter works better you have a bad earth.
But batteries do not like standing unused. When they get too flat they often will not take a charge as the charged/discharged chemical change can become permanent or one or more cells can be down. Try an optimate charger but also try a known good battery. It its too big use jump leads but with the old Punto battery disconnected.
If jump leading from another car don't run its engine as this can sometimes mess up the electronics.