Excuse me, computer professional here.
If you have blinking caps lock and num locks, it is CPU/GPU failing to function. It is very common in these line of laptops, which is pretty much all of the machines made in that generation (somewhere between 2003-2008 I assume). Sometimes its just the CPU, however ALOT of the times the GPU has poor solder points, in which you must get the motherboard "reflowed". Alot of people do the oven trick as well.
I have a dv7 which I am in fact going to do the oven trick as of tonight. It has the same problem. If I "preheat the PC" with no heatsink on, the solder softens at the GPU and causes a connection, if its a cold boot, no go.
You may or may not also have another problem in which you may have to check HPs Caps Lock/Num Lock blink codes. Usually both lights blinking once per cycle is CPU/GPU.
TL;DR? These HPs have the same problem XBo
60s use to have, the GPU solder is poor and needs to be reflowed.