[steven]

Okay, so I think I've figured out the problem. を, the particle, has quite a few uses... but in this case we are talking about one specific use (and in this use it can be interchangeable with が). Keep in mind, however, that there will be a change in nuance when they are "interchangeable". In other cases, one will replace the other depending on the kinds of verbs used.

The use of を which we are focusing on is that in which it is a "direct object marker", to use a textbook phrase.The problem is that most of us are thinking in English terms when we're playing with Japanese...

A couple examples of the usage of the を particle:
1) 私は社会を勉強している。 (I'm studying social studies)
2) 野村さんはやっとWiiを買った。 (Mr. Nomura finally bought a Wii)

Now as English speakers, we are all likely to think like this:
Because を is used as a "direct object" marker, then I can take any direct object in an English sentence and slap an を in front of it thusly:

私はボブの電話番号を分かる。→私は電話番号が分かる。
Since 電話番号　(or Bob's phone number is the direct object of 分かる, or what you know) is the "direct object" in English, we are likely to use を with it instead of が in this situation, even though が is better.

Another situation that can get you into trouble is this one:
私は彼女を電話した→私は彼女に電話した。

Again, since we are English speakers, all we see is me calling my girlfriend (or my direct object)... where in Japanese I think it's more of a transferring motion, if you will. So に is used instead of を.

I'm sure there are more examples that could be brought up, like 誰々と会う, but my point is that we are applying our English to Japanese. That is something that Native speakers don't have to deal with. My approach to dealing with this is to listen to as much Japanese as possible to help build an ear for what "sounds" good or not. It's like dissonance in music. If you hear something that clashes it will pop out at you immediately.

Back to the topic: を vs が

Like in my last post ~が/をのみたい... for 動詞+たい you can use either one, although there is a slight difference in nuance.

Also, for "potential", as I think the textbooks call it... it's a very similar situation.
Both アルコールがたくさん飲める or アルコールをたくさん飲める should work, but there will be a difference in nuance. I feel that を would be stronger. When I think about it though, I don't hear ～をできる often (or at all as far as I can recall).

I'm not sure about している/してある... If I think really hard I might be able to come up with a couple of examples for each... but I think が would be the safe choice if you are in doubt.

As a disclaimer, I'd like to point out that in "real" Japanese people don't constantly say "私は" over and over like that. Actually speaking/writing like that in Japanese isn't natural. I think this is an example of "negative transfer" when going from English to Japanese, by the way (all of this). The worst offenders, in my opinion, are the textbooks. By showing a couple of examples of how to use を and saying "direct object" and other fancy grammar-related words they are inducing errors on customers.

Also, I'm aware that the OP stated he or she is a beginner and that a lot of this might be too much to take in, but hopefully it will serve as a reference for anyone else reading. I always wish that someone had set me straight when I first started Japanese... I spent a long time un-learning a whole lot of misinformation years into my development. I'd also like to point out that I doubt my post is error-free... so if anyone wants to chime in on mistakes in my Japanese I'd appreciate it if you did so.