What is best to use for a desktop computer, 2 prong or 3 prong power plugs?
It's unsafe without the ground pin! You need to cut that damaged plug off and throw it away. And NEVER remove a ground pin yourself. The 2- to 3-prong adapters are meant to provide a ground via the tab and a screw, not to remove it.
What you're probably feeling is the switching power supply's EMI filter making the case &quot;float&quot; at roughly 1/2 of the AC line voltage. Without a ground, it's free to do that. With a ground, it doesn't, and that also completes the EMI compliance. Plus, if something goes wrong inside that would have made the case completely &quot;hot&quot;, the ground connection will trip the breaker instead of killing you.

Like Chris Stratton said in a comment to the question, your outlets may also be dangerously miswired.  A common form of that in the U.S. is called reverse-polarity-bootlegged-ground, where:

The ground and neutral that are supposed to run independently back to the distribution panel, are instead tied together at the outlet and a single shared wire runs back for both.  That's a bootlegged ground, and is hazardous enough already by itself.
In addition to that, the hot and neutral wires are also swapped.  If they're both black, like in old wiring in the U.S., or otherwise don't have a color code, then that's an easy mistake to make.

The combination of both factors gives you a ground pin that is connected to AC hot, in a way that a casual plug-in tester will NOT catch!  Touch that and a real ground at the same time, and you complete the circuit!
You say you're in the Philippines, so the standards might be a little bit different there, but physics still work the same for everyone.  Take the principles that I described and apply them to your standards.