There might be two reasons for this issue. Initially, the battery might be dead. In which case, you must replace it with a new one or charge it up in order to resume using the device. Secondly, the hard drive might be broken. This is a more serious issue and it requires the hard drive to be replaced with a new one.
For more information refer to [[Sony Handycam DCR-SR42#Section_Camera_won_t_turn_on|Sony Handycam DCR-SR42 Troubleshooting Guide]]