Central Locking Problems

[hmally]

I have an N reg Fiat Punto, 4 days, elec windows, central locking and alarm. The problem strated with my battery dying on me so I had to have the car jump started. The battery was still a bit dodgy but the car kept starting ok. Now the alarm and central locking have strated going off on their own. We've turned the alarm off and the battery is now working fine. However, the central locking locks and unlocks the doors as you are driving along. Even though I'm now having to lock the doors manually as turning off the alarm has stopped the remote central locking working the fcar can be locked when I leave it but it's unlocked itself when I get back to it. My partner has stripped the doors down and checked all the wiring but everything seems ok. Has anyone got any ideas?