OK. We are going to use a technique called Back Probing because I like it.
Its easy, and you can test the PSU when the computer is running.
Take the red probe. This is positive. Insert into the back of the 20/24-pin main molex connector. Start with a yellow (+12v) wire. Then, take the black Probe and touch it to the metal part of the chassis. This is ground.
The picture below shows using a ground wire, but I usually don't do that because from a textbook standpoint it is incorrect. Touch it to the chassis. It will still read correctly.
Repeat this process with the red (+5v) and orange (+3.3v) wires. I would also test the gray (Power_Good) wire as well. The Power_Good wire should be between 3v and 6v, but preferably about 5v.
As for the hard disk reading, my only guess is to try another SATA port. That is a strange issue. If you unplug the Western Digital, does it read the Seagate?
For the Thermal Paste, it won't make a huge difference TBH, but if you do happen to have Arctic Silver around, I would use that instead.
One thing I like about AS is the Arctic Silver Ceramique variety. It is completely non electrically conductive, so if you are clumsy like me and get some on the Motherboard, it is not a huge deal.