windows 7 - Laptop turns off immediately after power on

I have an oldish HP Pavilion dv6 laptop. The screen is busted so I use it for general media and server tasks. It's running Windows 7.

The machine has never given me an issue. When I turned it on this morning, it hung at the "Starting Windows" splash screen (the animation froze and there was no activity), which was strange. I held the power button to turn it off and when I tried to turn it on again, it stays on for about 3 seconds then shuts off. During this time the only things that really happen are the fan starts and the DVD drive powers up.

It runs off of AC power. The battery is not in great condition but it's not in bad condition either. I reseated both the battery and the hard drive (I recently used this machine for data recovery on some old drives and thought perhaps the connector wasn't seated right or had some junk in it). When I did this, the machine powered on again, made it past the Windows splash screen (I chose normal boot), then hung on a black screen. On reboot, it was doing the 3 second thing again. I think this partial "success" had more to do with it being turned off for a while than reseating anything.

I then left it off for about 10 minutes, turned it on again, and was able to boot into startup repair mode. It stayed at "attempting repairs" for about 4 hours then came up with an error that said "startup repair cannot repair this computer automatically". The problem signature was:

  Event Name: StartupRepairOffline
  Signature 01: 6.1.7600.16385
  Signature 02: 6.1.7600.16385
  Signature 03: unknown
  Signature 04: 1460
  Signature 05: AutoFailover
  Signature 06: 1
  Signature 07: NoRootCause
  OS Version: 6.1.7600.2.0.0.256.1

The repair log showed only one "problem", but not sure if it's actually significant as it's got that vague Microsoft "we don't know what's going on" tone:

  Root cause found:
  ---------------------
  Unspecified changes to system configuration might have caused the problem.

  Repair action: System files integrity check and repair
  Result: Failed. Error code = 0x490

After this, though, the machine rebooted and ran just fine (???), despite being hot and not having been turned off for very long in the mean time. The file system showed no errors.

The hard drive was in good health as of two days ago. At that time I had, coincidentally, run a SpinRite maintenance pass on it. There was nothing even remotely suspicious in the SMART data and there were no bad sectors or read errors on the drive. It still seems to be behaving well, so I don't think this is the issue.

I can't imagine that this is Windows or bootloader (I'm using GRUB) related, as the quick power off happens before any of this is loaded, around the time the BIOS splash screen would be displaying (I use an external monitor it takes just longer than 3 seconds to turn on when it receives a signal so I can't read anything that comes up immediately).

About a week ago, when I was doing data recovery tasks, I had the laptop in overheat situations a number of times (to the point of it locking or powering off), to the point where I had to stick it in my refrigerator to complete the tasks. I am wondering now, based on some of the answers below, if heat (or perhaps condensation or rapid cooling or large temperature differences across the device) could have damaged some of the components. It did run just fine for the following week but perhaps there was a "time bomb" of sorts?

What could have caused this, or how can I narrow down the cause? It happened very suddenly; everything worked great yesterday with no signs of trouble. I also can't explain why leaving it turned off for a few minutes causes it to be able to make it start to boot again.

Edit: Added startup recovery results.
Edit: Added mention of previous bad treatment of laptop.
Edit: Added post-recovery reboot results.

There are two probable causes:

• overheating - this can be solved if you open it up and clean the fans and heatsinks
• dry joints - this one most probably cannot be solved

It sounds like the motherboard is in imminent failure or it's over heating. It's pretty common for laptop heat-sinks to get clogged up with dust after a while. HP has a track record for over heating. I work as freelance it technician and have seen many of them running hot, plus a friend had one which pretty much fried itself to pieces.