I have seen many used systems which include worn buttons on the mouse and keyboard, food and drink stains, and of course, dirt, dust and grime. I too was a cat owner (I had two felines) however they never used the computer keyboard as a resting cushion, however they both used to knock the mouse off of my desk to get my attention when I was sleeping. A cute move, but of course not particularly desirable! (I would wake up and find my mouse hanging by its tail!)
To keep the keyboard clean, I first use compressed air (Dust-Off) to blow out dust in-between the keys. if you have ever opened a keyboard, you would understand how sensitive the contacts are between the actual keys and the membrane underneath. Cat hair and keyboards don't mix too well, so you might limit that with either a plastic or frabric keyboard cover (commercially available), or even by standing the keyboard on its edge up against your monitor when not in use. I wipe the keys to remove dirt with Windex, sprayed into a soft cloth or paper towel, (not sprayed directly onto the keys!!), and if you have let cat hairs and fur get under the keys, then you might have to open the shell and spray out the hair with the air can. When you reassemble it, make sure all keys make proper contact. Once you do explore what's underneath, perhaps you will appreciate that computer keyboards are not as durable as the old typewriter keyboards were, these having sensitive contacts and electrical circuitry. For hard to reach places, you might even use Q-Tip swabs instead of paper towels... again, spray onto the wiping device and not the keyboard directly. You don't want to get Windex deep into the under-workings of the keyboard and contacts.