Most power supplies use a ground reference for regulating the power output and conversion. Not presenting a ground reference is a Bad Thing.
There are also safety issues, possibly with the surge strip as much or more than the computer. I used to live in a very old building with marginal wiring and crappy grounds. I plugged in an APC power strip from the three-prong (but poorly grounded) outlet to to feed a lamp, clock radio, and stereo. After a couple days, I noticed a burning smell - it was the APC power strip melting down (it also uses a ground reference, and had none). It melted a hole in the carpet and looked to be on the verge of catching fire. APC doesn't warranty improperly implemented" equipment, and denies liabillity for damages caused by "improperly implemented" equipment.
The entire system needs to be properly grounded; failure to properly ground the system is likely to present some serious safety issues and damage to the computer equipment.
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Scott