Well, if the AI is not provided with extensive knowledge of the world, then it will be unable to do any of that, and even expression of desire to do that would be impossible. There is an often made argument that an AI which is factoring a large number would benefit from, for example, faster CPU clock speed; it won't as the goal won't be referenced to real world time in the first place, and to reference it to real world time would be hard or impossible extra work. AI's desire for extra memory looks like a better candidate, but when you consider memory modifications there's ones that just hack the problem solved.

-manipulate current through its hardware, or better yet, through the power cable (a ready-made antenna) to create electromagnetic waves to access some wireless-equipped device. (I'm no physicist so I don't know if certain frequencies would be hard to do)

There's a lot of capacitors and line filterson the power lines, so you can't get out any signal from mainboard itself. You might be able to do some low bandwidth FM at switching power supply's frequency by varying power consumption but no one will hear you because all the other computer power supplies pollute this range.

manipulate usage of its hardware (which likely makes small amounts of noise naturally) to approximate human speech, allowing it to communicate with its captors. (This seems even harder than the 1-line AI box scenario)

Full blown audio might be possible if you can change hard drive's head motion firmware.

-also, manipulating its power use will cause changes in the power company's database. There doesn't seem to be an obvious exploit there, but it IS external communication, for what it's worth.

Few bits a month that no one would extract and summarize.