Mainly because valuable files are at risk, I'm writing out everything I would do to get to them under the circumstances, at least one of which should work. Always back up your files as the HD can fail at any time.
Your external enclosure might not be working correctly, so let's go with the HP Diagnostics which say the drive is OK. Can you install the laptop hard drive in another laptop to try rescuiing the files with a boot disk? Perhaps the Win7 repair disk will work on that PC, in which case you can
Copy & Paste - in Windows Recovery Console. You could even
Adjust Win7 to boot on new hardware with Paragon Adaptive Restore CD for the purpose of repairing the install so it will start.
Download, burn to CD with WIndows Image burner, Boot the
HD Diagnostic extended CD scan
which should autostart without user input.
You could also boot
Partition Wizard to
Resize C Partition to make a space to do a rescue
Clean Reinstall Windows 7 that will give access to your files on the other partition, provides all the steps to get and keep a perfect install. If you had to do this with the hard drive installed in another PC because you simply cannot get the Win7 disk to start, you'd at least be able to rescue your files, then use PW to delete all partitions which will force the Win7 installation disk to autostart in the HP.
Make a bootable CD like was linked earlier or
Paragon Rescue Kit Free Edition 11.0 Free to try to copy your files out to USB. If you can get the Win7 disk or Repair CD to boot on the HP then you can
Copy & Paste - in Windows Recovery Console
If you can't boot a Repair disk then obtain the Win7 disk as discussed in Step 1 of
Clean Reinstall Windows 7 to work through the steps for
Troubleshooting Windows 7 Failure to Start.
If disks continue to fail to boot, try resetting BIOS to defaults:
Clear CMOS - 3 Ways to Clear the CMOS - Reset BIOS
If you want to report back results on the various steps, we might come up with others. I know that unless the drive was completely bricked (which should show up in HP Diagnostics) I would get the files out if not repair the OS to boot. Then the consolation is you get an install that is tons better than the HP Factory install which is worst in the industry, as long as you stick with the steps, tools and methods in
Clean Reinstall Windows 7 which has been used by over a million consumers without a single complaint or return with problems.