No, giving it as a present shouldn't work.
If it's in your sim's inventory, there should be a button above the wish panel. The button collapses with the little triangular icon at its corner, so you might have to click that to bring it back up if it's minimized. If the opportunity is completed, it should have a button to click that will say something like Return Computer and will result in giving your sim the command to find Joe Bob and give him his computer. If the button isn't there, it means the opportunity isn't complete. Are you using that to return the computer?