How to bring my personal desktop computer into Singapore?

You didn’t say about your purpose of visit!

If you are coming here as an employee then you can bring hard drive with you. If custom department asks then you can give the details about hard drive (no need to carry desktop screen or any other equipment).

If coming as a tourist then no need to carry such things here. Good luck

I have never heard about customs officrs checking a computer or questioning its content. I don't think they are strict - where did you hear that?
Of course it would be prudent not to have on your harddisk questionable political content (in the eyes of the Singapore government), porn or unlicensed software, but that is no different here than in most other countries.

True, custom officers normally don’t check here, I have encountered many times where custom officers ask to open your bags on food packets or gold ornaments related but that always in some other countries. Singapore doesn’t check that strictly. But, as Beppi said avoid carrying any materials related political motivated or disturbed speeches or child porn. You may get away carry such things (political speeches) in other countries but not here. Normal photographs, nobody will ask for a second.