No need for a lot of background. Suffice it to say I’m totally paralyzed and have to use an on screen keyboard to operate a computer. All full screen games overide my keyboard so I can’t enter any commands. Any help would be a godsend.
Try text-based adventure games. They tend to be complex and fun, without requiring difficult timing challenges or excessively complicated commands. Basically, you get a text description of what your character is and what’s going on, and then you type in a command, which your character will then do. Note that they are rather difficult in terms of winning, so if you’re just looking for a quick and easy experience, you probably won’t like them.
I’d note that Nethack is a rather different type of game than Zork and HGttG. Nethack is a roguelike game (genre named after the first such game, Rogue - inventive, yes?). In these games you play on an overhead view, with monsters/dungeon features/etc represented by letters and other characters. Typically the goal is to get to the bottom of the dungeon (with the dungeon becoming more dangerous the lower you go) and defeat the boss there. In Nethack, you also have to bring a certain amulet up out of the dungeon and sacrifice it to your patron deity, with the aforementioned boss reviving and reattacking you along the way.
These games are generally quite unforgiving - if you die, you have to start over from the beginning with a new character. Winning is a process of dying many times to figure out how the game works, and learn how to survive. They can be pretty intricate (see all the ways to kill yourself with a cockatrice corpse in Nethack).
There are many, many roguelikes out there. Another you might want to check out is DoomRL, based on the famous FPS Doom. Here’s a gameplay video with commentary if you want to see what it’s like without downloading anything.
Zork and HGttG meanwhile, are text adventures (or interactive fiction). As you might guess, they’re text based. Surroundings and things that happen are described in text, you type text commands to do things, and the results of your actions are described in text.
As a commercial genre, text adventures are thoroughly dead (Zork is from 1980, and HGttG is from 1984), but interactive fiction is very much alive as indie games. There is an annual Interactive Fiction Competition since 1995, and if pick one of the top rated games from any year, it’s likely to be good. For a random suggestion, try Photopia. Touching story (though considerably more linear than most IF).
I’d recommend old Lucasarts adventure games like The Secret of Monkey Island or Day of the Tentacle. They’re fun brain teasers with funny dialouge and interesting plots. Best of all, you only need to use the mouse to play them.
I believe ScummVM, the adventure game emulator, allows you to play them in windowed mode.
I third (fourth?) the Interactive Fiction option both for breadth of free games available and easy pacing. To give you a bit more information you need to install an “interpreter” which is a program that takes the rules for the game and presents it for you. I use Frotz which has versions available for any platform. Then you have to get the game itself and most of those can be downloaded from ifarchive.org.
Turn based strategy games are a very good option as well since you have a mouse and keyboard. Unfortunately as a genre it has almost completely vanished. The Civilization series is one of the last outposts of it for the PC.
If you’ve got a Mouse, that’s all you pretty much need to playConquer Club, an online game that’s pretty much the equivalent of playing Risk, but with tons of maps and all. I’d urge you to give that one a shot (it’s free but you have a limit of playing up to only 4 games at one time- games are turn based, and you have 24 hours to take your turn, but it can go much quicker than that), or if you choose to pay- then you can play unlimited games.