DV-6117dx - power light steadily blinking off-and-on and laptop won't work

Question

A little background:
A couple of days ago, I shut down my computer because it was a bit slow (nothing new installed beforehand).  Upon a restart the next morning, I got a "log on initialization" error (with the laptop screen not working and being able to see the error message on an external monitor only).  Too many hours with Google basically says the only real way around this is to reinstall the system.  Fine.  I tried the minimized image recovery twice - error both times.  Finally, I tried the full factory reset.  That worked.  After the reset, however, came an endless series of issues. 
- First reboot, keyboard and touchpad doesn't work so had to plug in external versions.  Moreover, the native monitor doesn't work so had to plug in my TV.  But the set-up for Windows did finish.  Once on the desktop, I tried to access the Window monitor/screen resolution menu to get image back onto the laptop.  Laptop beeped once and shut itself down with the power light (on the power button) steadily blinking but power button is nonresponsive otherwise.
- Tried a BIOS reset and got the laptop to power up.  Went into safe mode with networking.  Everything seems to work fine.  Restarted into normal mode (shut down then powered up, actually).  Boots into Windows on the native screen.  Went into Windows Update and that caused the machine to again beep and shut itself down.
- After a minute or two of steady blinking from the power button light, laptop powered on and looked like it went into hibernation instead of random shutdown.  Since the dialogue was still showing, decided to try Windows Update again.  Same result as last time with the beeping, random shutdown, and steady blinking.  This time, though, the machine hasn't tried to restart itself.
At this point, short of buying a new machine, is there anything I can do?  I do have access to a CD that I'll try but want that to be the last resort since it means losing the recovery partition.  Besides, with the recovery partition working well (keyboard, touchpad, native screen, etc. all worked beautifully dring that process), signs seems to point to some odd hardware issue.

Answer 1

I've run the full battery of tests allowed by my limited access. The only issue I've run into is concerning the BIOS, wherein it gave me a message about not being able to update/rollback due to not being able to read the BIOS image. Tried flashing it twice but failed both times. There appears to be some news on this particular front in that it might indicate an issue with my trying to restore the system so many times and confusing the BIOS instead of just some catastrophic failure.
In other news, I did get into the BIOS menu and reset to factory default. For whatever reason, that allowed me get the minimized image recovery to work whereas it never did before. Performed the MIR. All went fine until just now when I tried to restart the system (after a massive Windows update).
Upon reloading Windows, I got the same error that started this mess - Logon Process Initialization Error. Considering that an MIR is a pretty clean install and I only installed the essential Windows updates, I'm at a huge loss as to where this error is coming from.
In any event, since there was no way to shut down the system, I had to do a hard shut down. There was a few minutes of waiting because, now, my power button is no longer functioning as it should - as in, it seems to only power on the laptop at my prompting when it deems necessary, not whenever I push it.
Moreover, having just rebooted with a clean boot (disabling all but MS services), my screen and touchpad both shut down and an external monitor and mouse were required. This seems to point to a graphic card issue, but it's a weird issue since, unless I'm booting into Windows normally, I've never had an issue with either the touchpad or screen through this whole mess - even booting into Safe Mode, I only encountered this issue once and only during the midst of the mess when the laptop was undoubtedly a mess.
At this point, I'll probably try to boot into this current Windows install once or twice more before giving up and installing a fresh copy of Windows (have a CD), losing my recovery partition. Honestly, considering the loss of the power button's reliability, this seems like it's just a brick that occasionally rouses itself to be more.  I'll report back with news of the clean install just in case anyone else ever runs into this special unicorn of a problem, but it appears my issue is a lost cause.
Frankly, I'm just annoyed at HP at this point. Leaving aside the fact that the warranty seems to have started over a month before the laptop got to my hands, this laptop top is just a couple of months out of warranty. I don't expect hardware manufacturers to guarantee their products for life, but the hardest thing running on this machine was Office (well, SETI@Home for the last 2 weeks). It was sitting elevated on a desk for the entirety of its life, and the CPU barely ever surpassed 50% usage. Every month or two, the vents would get compressed air sprayed in to get rid of excess dust. The only hardware change was done before the laptop ever turned on and that was a RAM upgrade. What I'm trying to say is that this was a laptop that should have given me, at the very least, more than just a few months of out warranty in terms of usage, and even if it dies, it shouldn't have been some catastrophic failure as this appears to be.
PS None of my blinking corresponds to the HP list of blink codes. It's my power button that's blinking, not my caps button light or wireless light or anything like that. And it was a steady blink off and on. Moreover, the blinking is no longer occurring since the successful MIR.