Hi Idpdrdr,
Have you tried the following:
1. Re-seating the DIMM (RAM) modules.
2. Starting the laptop with the power adapter connected and the battery removed.
3. Starting the laptop with the HDD and ODD removed. (to see if it starts normally, (even if only to get into BIOS) up to the point where it says no hdd detected or something similar.
4. Have you tried connecting an external monitor to see if there is any display at all during start procedure? (can you see the 'backlight' of the lcd screen in your laptop?)
Here is a link to the service manual which shows how to remove / install the memory and how to remove the HDD and ODD. Be sure to do this with the power disconnected and the battery removed.
https://download.lenovo.com/UserFiles/UserGuide/en/User's%20guides%20and%20manuals/G460-G560/Lenovo%20G560%20Hardware%20Maintenance%20Manual%20V2.0.pdf
If your laptop is running I recommend that you 'create a system image' and save it to a USB HDD. That way if you want to try things at least you can restore your laptop to what it was, before you started troubleshooting, once you have hopefully found the problem.