On the assumption that the immobiliser has developed a fault, one solution is simply to buy a chip for the ECU which by-passes the immobiliser.
the car just would not start at all didn't make any noise and lights came on but very faint
and the fact that it did start, but with the CODE light on lead me to think it's not the CODE box which is the real issue.
I would:
1. Get the battery stress checked -- many factors will be happy to do this for free.
2. In the meantime, try borrowing a known good battery from a friend/neighbour, etc. Take your battery out and pop this one in instead. What happens?
3. If 1 and 2 make no difference, undo the main earth leads, scrape clean, coat with vaseline, re-attach. One runs from the battery negative to the wing, the other from the wing to the top of the gearbox. Both are black, close to 1cm in diameter.
I've put a link to this from the Cento section as the Mk1 Punto section is rather moribund at the moment.
If you let people know
roughly where you are, some kind soull might be willing to come and take a quick look.