Considering the age of the machine replace the cmos battery......just to cross it off the list.
If it still won't boot do you get a bios splash screen?
My desktop, HP Pavilion p7-1236s, will power on but it will not boot until I’ve powered it off and on between 5-20 times. No beeps, no blinking lights. When this happens the power lights are on, the fans are on, the amber light under the hard drive icon comes on but just for a second, the hard drive “clatters” for a couple of seconds, then nothing else happens – no boot. Like I said, after powering it off and on 5-20 times, it finally boots. Once it’s running I don’t shut it down. But another problem occurs: eventually it freezes for no apparent reason and I have to power it off. And the cycle starts again.
Here’s what I’ve done to try to resolve it. I tried the troubleshooting steps on HP’s support site for “Computer Does Not Start”:
•Removed discs and devices – only monitor, keyboard, and mouse connected
•Performed hard reset
•Cleared CMOS
•Ran hardware diagnostic tests (F10) – all passed. Could only run this when I got it to boot.
•Checked for hard drive detected in BIOS - detected. Could only run this when I got it to boot.
In addition I cleaned out dust inside of computer – heat sink and fans had a lot of dust. I also reseated RAM and hard drive power & data cables.
I also tried a known good PSU but still the same problem.
Would appreciate any suggestions on what else to try to resolve this problem. Thanks!

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