Monitor goes black after power on.

May i know, is it a crt monitor or lcd monitor? If it is a crt monitor, then you can try to check the dry joint on te pcb board especially primary and secondary power supply. After that check the FBT with blue ring tester & cap meter to check their HV cap value.

If it is a LCD Monitor, please check on inverter board and the ccfl lamp too. Please check all the electrolytic cap on lcd monitor pcb board for low esr ohm with blue esr meter. Below is some usefull link for repair lcd monitor and crt monitor:

1) www.FastRepairGuide.com
2) www.fastrepairguide.com/recommend/lcd-monitor-repair/

Hope this help.

To your success,
Kent