Your HP Pavilion 1275MX will not turn on after you press a start button. It lights up then you can hear a fan and disk turning, then it will stop. Nothing on a screen and then some lights start to blink.
One is above a scroll key and another is next to a caps lock key. You tried removing a battery and power supply but get same results. You bought that laptop from QVC and it came pre loaded with no CD or recovery disk.
You have tried a removal of that power supply, battery and holding down a start button for thirty seconds. You tried starting it up and holding an F10 key. I think you might have a failing memory stick. Can you try reseating your memory sticks.
If you have more then one memory stick, try testing one at a time until it boots properly. Shut down that computer and close a display. Disconnect all external devices connected to that computer.
Unplug that power cord from an AC outlet. Turn that computer upside down on a flat surface. Remove a battery from that computer.
Loosen that memory module compartment screw. Also, here is a manual for that HP Pavilion 1275mx computer with same instructions I gave you. You can follow instructions starting on page 7.
Lift that memory module compartment cover away from that computer. If you are replacing a memory module, remove that existing memory module. Pull away retention clips on each side of that memory module.
That memory module tilts up. To prevent damage to that memory module, hold that memory module by edges only. Do not touch components on that memory module.
Grasp that edge of that memory module, and gently pull that module out of a memory module slot. If there was only one memory module installed, can you reinstall it in a different slot. There should be two memory slots in that computer.
Try installing that memory module in a different slot it was initially installed and then try to boot that computer. Please try booting it with a bottom module still installed. You don't have to put your laptop battery back in, just place cover over that RAM if you want and then try to boot it up now.
Take out memory in bottom module and install it in top module and see if it will boot properly. Try to boot that computer with only one memory module at a time. I'm thinking it's either a bad memory module or a bad memory slot.
Those blinking lights near caps lock and scroll keys indicate a bad memory stick when I searched on the Internet. Please test those memory sticks one at a time. If they both don't work in the same memory slot then that slot is bad and then you try testing both those memory sticks one at a time in second memory slot.
If you only had one memory stick installed in that computer, then please try testing both memory slots with that one memory stick. You want to make sure to rule out it being a bad memory slot. Try testing each individual memory stick in the same top slot?
If neither memory stick works in top slot it is probably a bad slot. Then you test each individual memory stick in bottom slot. Sounds like bad memory if they won't work in neither slot.
Your data on your hard drive should be ok. I recommend taking that computer to a local computer repair shop. They will be able to test whether it is bad RAM or slots.
Some will diagnose it for free and then tell you what needs to be done.