And especially the part in bold, though for me that's sometimes tempered by the jolt of losing immersion as I have to pop back out of the game and into the options menu or the manual to look up controls / key commands.

I have nothing but free time, but it is often difficult for me to start a game.

A lot of the time I am just too depressed to play anything at all. As much as I love video games, some days my brain just doesn't want to cooperate. And starting a new game that I haven't played yet... That is like committing to put a man on the moon. I'll have to learn the controls, the mechanics, the story... It is just too daunting sometimes.

Luckily I seem to be taking a turn for the better at the moment, so I'm playing everything I can right now before I hit another depression.

Nope, I don't have trouble starting new games at all. I have trouble sticking to all those I started and then took a break from at the slightest hint of frustration or boredom. You will never see me replaying games like Baldur's Gate, but, alas, I have a huge backlog of half-finished games. ;)

Your missing some great games because of that and you don't need to. Try my way: define yourself goals which you want to achieve in a particular game of this kind. It's not hard to do it once you have an idea what a certain game has to offer. Examples:

(A) In a fighting game a goal can be to finish the Arcade Mode (Story Mode) with a character of your choice or even finish the game with all the characters.

(B) In a racing game it can be: try every track and every car there is in a game. Just draw a table on a piece of paper with names of tracks and names of cars and fill the entries so you know what you have done already :)

(C) In a MMO a goal can be to see every area there is in a game. For example: start making screenshots and the goal can be to make some cool screenshot in every location.

Once you get the goal done you can put the game away and note all the new ideas for goals in your "gaming diary", so you can return sometime later and do it if you're in a mood.

Games are an amazing things to play with. In most of them, only your imagination limits your fun. Can you recommend anything like that? I'd be interested if it was not too expensive and definitely it has to be an offline application.

Solution.
1: Uninstall and delete any backups of those games.
2: Don't buy any more games for yourself.
3: When you do, force yourself to spend an equal amount on someone else / something charitable so its no longer so much of a "bargain buy"
4: You are now set to attempt some of your backlog games.

I have a play list of 20 games, one of each genre or sub genre. When I achieve something in one of them (finishing a level, beating a boss etc) and I don't want to continue I go to random.org and select a random number between 1 and 20 then play the game that corresponds to THAT number and so on, until I complete a game at which point I record my achievement in the current
Games finished in 20XX thread
http://www.gog.com/forum/general/games_finished_in_2014
then go to my backlog list for that genre, see how many games are listed there and type THAT number into random.org to select a replacement game for the list!
It's actually like a game-playing meta game - works for me!

I don't really have a problem with buying games and not playing them.
Sometimes the price is just too good to let it pass, so I'll grab this interesting experimental game for one buck and try it out... if it's good, cool. If not, hey, you've paid way more many for stupid stuff in your life before.

If I can buy a ticket for the cinema for ten bucks, and not enjoy the movie, without feeling bad about it for a long time, why should I care so much about my backlog?

And most of the time I see it as another collection anyway. Collecting music, movies or books is also expensive as hell, but sometimes to have this neat little game you played as a child is enough satisfaction.

There are a few promising software packages I've come across for this sort of thing, although they are all missing something that I'd ideally like it to have. I'm thinking about writing my own program at some point so I can have all the features I want, but in the meantime I've just been using a highly customized OpenOffice spreadsheet to maintain my collection. Since it can easily be exported to .csv in this format, it can then also be easily imported into a true database when the time comes.

You might want to give these solutions a look and see if one fits for you:

Sisimizi Game Catalog: This is a derivative project from the ANT Movie Catalog, a very lightweight and simple tool but highly extensible and easy to customize. It is free and open source, as it is based on the open source ANT Movie Catalog.

Collectorz.com: These guys have crafted a pretty nice suite of collection database software, and also now have standalone + online management capabilities. The only issue I have with these are that I'm a cheapskate and feel the software is a little expensive, particularly since they charge separately for each type of collection you have and also charge a recurring fee if you want to use their cloud service.

Play games with a clear road to a clear end. Stick to that game until you get bored, stuck or have finished it. Then start a new similar one.
The games you listed are not like this. I understand you because I too like games with lots of choices. Problem is I rarely finish them. ;)