What general rules govern the usage of "by" versus "through"?

What general rules govern the usage of by versus through? For example, which is correct in each of these cases:

My house is heated by/through gas.
I'll send it to you by/through mail.
I'll pay you by/through check.
I learned that by/through a lot of practice.
Success only happens by/through hard work.
The tickets are available by/through the Internet.
Through/by including a warning prompt prior to asking a SA related question, SPAM probes have been thought to isolate workload from the assessment of SA.

I found the majority of these by/through a Google search, but the answer there was equivocal.

Through generally indicates transit from one end of something to another (often, but not always, the opposite end). This can involve literal passage through space or time ("We drove through Texas", "I waited through the night"), or figurative movement through a system or process ("Your request is still making its way through the bureaucracy").

By as a preposition has many definitions; the ones that interest us all loosely boil down to "using the means, mechanism, or agency of." If means or mechanism don't sound very different from system or process to you, don't feel bad. These are two of the more difficult prepositions to get right, and sometimes there is no right answer and you just use the one that feels right (or less wrong, anyway). Writers and editors argue over this and related matters all the time.

As a very general rule of thumb, if literal or figurative motion or progression is involved, use through. Otherwise, use by. There are tons of exceptions, however, and sometimes you just use whichever preposition is most conventionally used with the word or phrase, without asking questions.

To look at your examples specifically:

• My house is heated by/through gas. (Gas is the means used to heat your house.)
• I'll pay you by/through check. (A check is the mechanism you use to pay.)
• I learned that by/through a lot of practice. (Practice is a process, and you progressed through it from the point at which you did not possess the skill to the point at which you did.)
• Success only happens by/through hard work. (Hard work is a process, etc.)
• The tickets are available by/through the Internet. ("Through" is a bit of an evolved convention here. Think of the Internet in the popular 1990s-era conception of a virtual realm through which you travel to your destination.)

Those are the easy ones. The other two are harder:

• I'll send it to you by/through mail. (This depends on whether you consider "mail" to be a mechanism or a system. Generally, I would either use by mail or through the mail, with the idea that "mail" is a mechanism, but "the mail" refers to the postal system.)
• Through/by including a warning prompt prior to asking a SA related question, SPAM probes have been thought to isolate workload from the assessment of SA. (ugh, this is just an ugly sentence to begin with; I'd use by including or through the inclusion of, with similar reasoning to the above.)

My local dictionary helps point out the difference:

through - by means of (a process or intermediate stage)

by - indicating the means of achieving something

Each word has a host of other uses but these are the closest match. The key is the note of an "intermediate stage" with "through". Through is most applicable when the means is merely one step of the process:

I'll send it to you by/through mail.

"Mail" is the intermediate step; the end step is receipt of the object. For comparison:

My house is heated by/through gas.

"Gas" is not an intermediate step. It is the source of the heat.

Using this distinction, one could theoretically use "by" in nearly every instance where "through" would work; the converse is untrue. You could not use "through" everywhere you could "by":

My house is heated by gas.

I'll send it to you by/through mail.

I'll pay you by check.

I learned that by/through a lot of practice.

Success only happens by/through hard work.

The tickets are available by/through the Internet.

Through/by including a warning prompt prior to asking a SA related question, SPAM probes have been thought to isolate workload from the assessment of SA.

Generally speaking, however, "through" will usually hold a more accurate connotation that redirects the focuse away from the means. Saying "success happens through hard work" implies that "hard work" is the intermediary process and not simply an end in and of itself. In other words, it is more typical (and sounds more correct) to use "through" when possible:

I learned that through a lot of practice.

Success only happens through hard work.

This is mostly due to the other definitions that "through" reserves. In this case, "continuing in time toward completion of" is also included in my local dictionary as a meaning of "through".

The final examples are somewhat of a toss up:

I'll send it to you by mail.

I'll send it to you through [the] mail.

These are both acceptable (although I would add the edit in the latter) and mean roughly the same thing. The former slightly emphasizes the method of delivery; the latter focuses more on the act of sending and receiving. The same is true of the Internet example.

Through/by including a warning prompt prior to asking a SA related question, SPAM probes have been thought to isolate workload from the assessment of SA.

Again, if the intent is to focus on the method, use "by"; otherwise use "through".

The summary:

• use "by" when "through" does not work
• if "through" has a specialized definition for that case, use "through"
• otherwise, use "by" when focusing on the method; use "through" when focusing on the end result

Without any reference whatsoever, I would suggest as a general guideline that "by" is used when you use (or could use) a gerund. "Through" is used otherwise. So for your list:

My house is heated by [using] gas.

I'll send it to you by [using the] mail.

I'll pay you by [using a] check.

I learned that through practice. OR I learned that by practicing.

Success only happens through hard work. OR Success only happens by working hard.

The tickets are available through the Internet.

By including a warning prompt... OR Through the inclusion of a warning prompt...

I feel it's worth mentioning that while you might think of saying

The tickets are available by using the Internet.

I think the availability of tickets cannot be made to happen by using the Internet. But you might say

Tickets may be purchased by using the Internet.

And again, I have no grammar reference for this; it just seemed right to me. Anyone?