Is the HDD causing computer slowdown?

I bought a new computer about 3 months ago. I took the fairly new, 1 TB HDD out of my old one and stuck it in an external case to be used with my new one.

I had an old 40 GB seagate barracuda HDD that was salvaged from a junk Dell workstation. Probably a year 2001 or 2002. I put the HDD in my old computer and installed Windows on it. The computer has a 1.6 GHz Pentium dual core and 2 GB of RAM. It is running extremely slow. I know this computer was never as slow as this. Can an old HDD slow down a computer to the point of making it practically unusable?

I have a Chromebook running Ubuntu 13 with a 1.4 GHz dual core celeron and 2 GB of RAM and it is quite a bit faster. It is a Haswell though, not sure how much difference that makes.

Is it possible that I’m finally realizing how slow the old one really was? You know, kinda like playing PS1 games after playing PS2 games?