Default Motorola Razr not turning on

The battery of my phone died some months back and recently I bought a new battery. The phone used to turn on with the earlier battery but never used to last without charger. Now I got the new battery installed it doesn't turn on. When I plug it in the wall charger, the motorola logo appears and the battery sign appears with 0-5% battery everytime and it vanishes in 5 seconds.
I don't have a factory cable.
Is there any other way I can turn my phone on?