Hey try this simple steps, which in most cases solve the problems :
1. Remove the charging cable and remove the battery, first try and start it only with the cable, then with both.
2. Sometimes, due to usage, the monitor connection can go wrong. Ho ahead and play with it, close it, open it, and so, see what happens.
3.Perform a hard reset by removing the small battery on the motherboard, this will reset all the settings of the bios to the factory ones (may not work in some cases, due to anti theft policy, but worth a try).
4. (be sure it's not the monitor) Plug it to a router via lan, and check on another terminal if the PC is booting and connected, if it does, we found the problem, if not, then its not the monitor.
5. Format everything, but this is more complicated and is better if you take the PC to a pc master.