GFCI outlets are for protecting human life. They detect any current imbalance between the hot and grounded ("neutral") conductors, and trip very quickly when any imbalance is detected. When any load is connected to the circuit (like your running computer), the hot and "neutral" should carry precisely the same amount of current. If the current is different, that means current is flowing through some other path. If that other path is your heart, you're a goner.
So a GFCI will provide human safety on an ungrounded outlet. If you install a GFCI, one GFCI can protect all the outlets "downstream" from it, and if it is on an ungrounded circuit you're supposed to put the little "No Equipment Ground" label on it. This does allow you to safely put 3-prong receptacles on an ungrounded circuit.
A GFCI cannot provide grounding for equipment. That's a different matter. Proper grounding serves a lot of purposes. One purpose is reducing background noise or "hum" in electronics. Grounding also helps surge protectors work more effectively by giving them a path to shunt overcurrent to, although a surge protector also has one or movemore MOV's (Metal Oxide Varistor) which divert current. MOV's do wear out and can eventually fail if they're hit too many times with overcurrent.
Also, with your computer case, all the pipes in your house, the housings of all your other grounded appliances and so on set to the same voltage potential, there isn't a big voltage differential if you touch a faucet and your computer at the same time. If you shuffle your feet across the carpet then touch your computer, a proper ground gives that static electricity (which could be 10's of thousands of volts) a non-destructive path that shunts it away from super-sensitive CPU's and memory chips. Grounding does provide a degree of human safety, as well. If there's a short in the device which energizes the casing, and you touch the casing, the ground wire is an easier return path for the current than you are, so you don't get electrocuted, and so on.