First, stop thinking like a mage, a caster of spells, start thinking like a maker of magic doodads, like Butters (and Bob!).
OK, now you realize that the problem is not that you can't use computers, they work fine, you just can't be next to them while you do it. So, how do we use one from way over here while it is way over there?
First, you must have a large enough place that you can have the computer at one end of a long house, say a wing, or in some way well away from any mages, and in a rather long rectangular room. You use it from one side of the room, the computer is 20+ feet away at the other end.
Seeing the screen- This is the easy part, use a projector, and project the screen onto the wall at the end of the room the computer is in. This way, the screen will be big enough that you can see it from across the room.
Controlling the thing- Keyboard, have one, push key, it is simply a regular looking keyboard that merely connects one big solid piece of metal to another, a simply on/off switch, for each key. From that, a series of wires runs to the actual keyboard, above which is a series of solenoids, when the switch is pushed, power goes to the solenoid, which then extends a rod to push the actual key on the actual computer keyboard, one for each key. You will want surge suppressors on each wire, just in case...
Next, make that computer have two screens, the other is a touch screen, which shows the same thing the projector does. Now, have a similar series of solenoids spaced about the screen to touch it when you push a button at your end.
You now have a touch screen and keyboard controlled computer, good enough. Sound, well, hook up big speakers and have them shout at you from across the room (it is only 20 or so feet).
Possible additions: It would be good to have some sort of circle or barrier to magic energy between you and the computer. This will have to be self powered (like Marcones desk circle, or Harries wards), it does not have to be very powerful, just enough to stop stray magic eddies, or spells cast in another part of the house.
Other things, a magic wireless keyboard, magic headphone, or a magic powered mouse, and a much smaller remote screen, may be possible, but will take a lot of work, and are probably not worth it. The screen is easiest, just use a magic seeing eye or mirror, put it in front of the computer screen, it will transmit to a magic mirror were you are what is on the screen, doable, but you would have to make one, and the projector is available now. Magic keyboards/headphone/mouse would depend on using a magic crystal tuned to put out radio or IR signals identical to those put out by wireless versions of keyboards and headphones and mice, the problem being to shape the signal into something the receiver and computer will understand, which will take some knowledge of wireless technology, as well as some considerable work to design a magic powered processor to process the signals (which send commands to the crystal, which turns that into IR). The keyboard would be fairly simple (comparatively), headphones harder (as long as you don't mind AM radio quality sound), and the mouse would take some work, and probably only give you an old fashioned analog quality mouse.
So using a computer is possible, as long as you have a big house, or better a headquarters, the White Council HQ could set this up and have at least one computer available for use.
