Proofreading is useful, so have some of my time. Or skip to last paragraph.
Now for the downside: I'm not looking for the position in your job posting. I'm much more inexperienced (I believe the business term is "cheap to hire[no period here]") than you want for that position[, and - period here. runon] I'm a junior in high school looking for a summer job working remotely - [, as ]relocating is unrealistic given my age.[avoid brackets] I would be able[really?] to perform the Rails and Java work [that you want done - remove], but I would do so from my house[you've mentioned this], and after summer[, no comma here] I would have to drastically reduce my hours. [I would need drastically reduced hours?]
I hope that my lack of job experience and inability to work permanently do not prevent you from considering me. I have solid knowledge of how to program[I am a capable programmer?] (see my resume for AP tests and projects [that prove it - awkward][. parenthetical notes don't get their own periods])[avoid parenthesis unless it's just a side note/quip]. I could be a jolt of energy helping you get a few new, cool features out the door. I also have a business-oriented facet of[to] my mind, so I could help think of [premium - don't need this] features that people would actually pay for [that would generate revenue, etc.] or possibly even float other business models[I hope you have serious credentials to back this up].
As a high school junior, I am looking for a summer job working remotely. [After summer,- move this...]I would be able to continue on a part-time basis [after the Summer [when classes resume]]. While[Though] I plan to continue my computer education in college, I have solid knowledge of how to program right now (see my resume for details). As a young person[you think older persons aren't "jolts of energy"?], I could be a jolt of energy helping you get a few new, cool features out the door.
Not bad overall for writing. It lacks tact in a couple of places. You need to make these of similar length, content, and quality if you want an accurate comparison.
I prefer A, ending right after "than you want for that position", followed by B. Make it casual but terse.