Check batteray first, try to turn on with a good batteray, if still problem :
1. Try to charging the cellphone
2. If the cellphone can be charging, probably power switch fault/broken
3. Check power switch first, replace with a good one if needed.
4. If the problem not solved, try to flash/upgrade software/firmware with a latest version
5. If the problem still not solved, resolder flash IC, replace if needed.
6. If the problem still not solved, probaby main engine/pcb broken.
7. Trace for broken circuit or swap engine.