Tilting my computer while on

As long as you don't slam it, there is no problem. The only moving parts are the fans and hard disks. The fans aren't that delicate and the hard disks are usually rated for over 50Gs of acceleration while running (this is quite a lot).

The real problem with moving the PC around while it is on is the risk of tripping it or disconnecting some cable you didn't realize was stretched out.

Reference for the disk shock tolerance:
http://www.tomshardware.com/reviews/a-sturdy-companion,758-2.html
 


Consider a laptop. Turn it on, pick it up, turn it on its side, put it in your backpack.
No issues.

Laptop drives are nothing special.

Now...if you drop it while it is on...issues.