Here below are possible causes and troubleshooting steps of laptop that can't power on, hope it may help:
1. Dell Studio 1537 AC adapter
2. Dell Studio 1537 Power jack failure.
3. Dell Studio 1537 Motherboard failure.
Possible troubleshooting steps and repair solutions:
1. Test the AC adapter with a digital multimeter. It's possible that you have a failed AC adapter. If you don't have a multimeter, test your laptop with another known good AC adapter.
2.It's possible that power jack (socket where you plug the AC adapter) is broken. Remove the motherboard and take a closer look at the power jack. In some cases you can fix the jack by resoldering it on the motherboard. In other cases you have to replace the jack with a new one. Using a multimeter, test if the power goes to the motherboard through the jack.
3. If replacing the AC power adapter and jack on the motherboard doesn't help, most likely you have a bad motherboard. Replace the motherboard.