Its unlikely but possible your new battery has failed. It is more likely that it has got really discharged by being stored for the 3 months without getting fully charged. A few starts and a bit of running now and again wont put a battery back to a full state.
The Mk5s and other similar cars need quite a high minimum voltage to start. Turning a cold engine over with a part discharged battery will probably lower the available voltage to below starting voltage. Even a Jump Pack may not be sufficient - as you found!
Try using a jump start from a car, with the engine running, using some heavy duty leads and leaving the 'jump car' running for about 10 - 15 mins with the leads connected before you try to start. This will get some volts back into the dead battery.
Ideally, of course, you should bring the 'dead battery' up to full charge first, with a decent mains battery charger.
If you do need a new battery, search on here - there are quite a few threads on types, capacities etc. From memory - I think you need at least 72 amps capacity and minimum CCA 650 amps for reliable cold starting. If that's wrong someone will correct it!!!
Good luck!
