Laptop unusually slow after being accidentally dropped. Hard drive was replaced but still slow

Question

My laptop—a Dell 1747 i7 laptop—fell from my desk to the concrete floor of my basement office when my son tripped on its cord. As would expect, that was it for the hard disk. Luckily, though, the screen survived and shows no signs of damage. Yet, I have been experiencing a strange performance problem ever since the incident.

After replacing the hard disk, I have been unable to reinstall an OS. I tried reinstalling the Windows 7 it came with, and I also tried installing Ubuntu. Neither install crashes—but both take hours and hours to load / install. Even when I run the built-in memory test, a test which the diagnostic software claims will take 30 minutes, it took overnight to finish.

So far, I have completely broken down the system, including removing the heat sinks, and re-seating the CPU. Then, I reassembled it and tried again. It doesn't appear to be running any better now.

While I was disassembling it, I inspected each component and found no other evidence of physical damage. No sign of flexing or cracking In the circuit boards. Do discoloration sign of overheating. The only thing unusual I found was a bit of foreign matter—like clear plastic wrap—covering the base of 3-4 pins of the CPU—near the square void at the center of the chip.

Does anyone have ideas on what may be wrong or what I might try next?