Here's what the system settings are showing me. They are the same for both when the HDD is in the old computer and when it's in the new computer
KDELibs Version: 4.13.3
Qt Version: 4.8.6
Kernel Version: 3.13.0-116-generic
OS Type: 32-bit
It's also only showing 3.8GB of ram, but I have 16GB installed, and it's recognized in bios as 16GB
One other thing I did was grab the latest version of Kubuntu 14.04.5 LTS and installed that onto my SSD in the new computer. During installation the PC name comes up as "SMBIOS implementations newer than version 2.8 are not fully supported by this version of dmidecode." I noticed this happening before, but I didn't think anything of it at the time. This may be the root of my problem.
Also, I know I downloaded the 64bit version of 14.04, but after installation, the system settings come up as 32bit version, and again only seeing 3.8GB of ram when there should be 16.
My motherboard has UEFI BIOS, and doing a quick google search, I find that there's been a lot of issues with installing many different version of Linux on UEFI boards. There does seem to be some workarounds, but I'm going to keep researching for a bit. But if anybody has any quick fixes, I'll take them.
Thanks