Dell Inspiron 3521 is impossibly slow, even after formatting, and even while attempting to boot externally

The problem, simply stated, is that my Dell 3521 notebook has become so slow that I can't even successfully boot from it, not from its internal hard drive and not from an external USB drive with a bootable copy of Windows 7 or even Hiren's BootCD.

Details:

A few weeks ago, the laptop, loaded with a Windows 7 OS (with an up to date copy of Avast Premium), became so slow that I couldn't practically timely complete even such basic tasks as copy and paste operations. Attempts to restart the machine would randomly produce the Windows Boot Error as well as randomly, but extremely slowly, successfully boot at other times. Moreover chkdisk showed no file system errors.

Attempted Solution 1:

Suspecting corruption of some OS files, I used a bootable Windows 7 copy to replace the OS. After doing doing so, the speed seems to have returned to normal for a while but in the course of a few days, it became just as slow. In addition, the Windows Boot Error when attempting to restart also randomly occurred.

Attempted Solution 2:

Suspecting malware or a virus, I scanned the machine with programs such as Hitman Pro in safe mode (safe mode was slow, but not as slow as normal). No malicious programs or activities were detected.

Attempted Solution 3:

I decided to format the partition on which the OS was installed and clean install Windows 7. I figured that if it was a hard-to-detect virus, I could get rid of it that way. After the install things seemed to have gone back to normal; however, the slow state returned again gradually after a few days. I performed a few more reformats and reinstalls but this pattern persisted: it would initially be OK but then deteriorate in a few days to its slow state. I did note that with each reinstall, the time it would take to become slow would significantly reduce. And the number of Windows Boot Errors on attempted restarts would increase.

Attempted Solution 4:

Fearing an impending hard drive failure, I decided to back up my most important stuff in the other partitions immediately after a reinstall. However, the condition had gotten so bad that I couldn't manage to back up everything and when I attempted to restart, the Windows Boot Error (0xc00000e9) became consistent.

Attempted Solution 5:

I decided to use USB-loaded Hiren's BootCD tools to attempt to recover my stuff before proceeding further with any other possible interventions. While the main menus for the program would load well, attempts to load into Mini Windows XP failed because the boot process was so extremely slow that I waited for hours with no success. Attempts to use such tools as TestDisk to recover my stuff were also undermined by the impossible slowness of their accessing the contents of the hard disk.

My Tests:

• I used Dell's ePSA Pre-boot System Assessment Tool to check the health of the machine and the results were all fine except for the hard drive test, which was reported as not having completed.
• To check my hard disk's health with another tool, I used the MHDD tool in Hiren's BootCD to check for S.M.A.R.T values. Astonishingly, the values seemed within he ranges of good health for the drive. Moreover, even though they were extremely slow to do so, some tools in Hiren's BootCD are able to load the hard drive and I could see that my stuff was well and intact. However, attempts to copy any of my data to an external storage device failed because of the extreme slowness of the process.

I need a way to recover my stuff and/or a solution to the slowness and/or recommendations on how to proceeded from here.

Short of throwing this straight to How can I remove malicious spyware, malware, adware, viruses, trojans or rootkits from my PC? it might be worth checking a new drive - in isolation & as part of a restore.

So, broad strokes...

• Swap in a brand new HD [or SSD to be a bit future-proof]

• Install a fresh, clean OS - don't import any old data. Install any needed apps from their original source, not from backups.
  Be patient with this for a few days; importing any old data at all will negate this part of the test.

• At this point, if you have another guaranteed-clean drive you can do a fully-restorable backup to, do it. Otherwise you may need to later blow this away & start from scratch again.

• Test for a week, see how your perception of speed goes.

• If it slows down, you may have a hardware issue other than the drive itself.
  If it doesn't, then now is the time to potentially burn the new OS [which is why we did the full clean backup before we did this bit]... restore from your old drive anything you can't live without.

• Test for another week.
  If nothing slows down, your old drive was dying. If it does, you have to burninate your old data. Nuke from orbit. Refer to How can I remove malicious spyware, malware, adware, viruses, trojans or rootkits from my PC?