Aleh, I may be wrong, but I believe that кто-то refers to a specific somebody, whereas this person will take ANYbody (кто-нибудь).

Кто-то пришёл. Кто-нибудь пойдёт в кино? We can't say: "Кто-нибудь пришел." when stating someone's arrival. But I would possibly say: "Кто-то пойдёт в кино?" meaning the same thing as with кто-нибудь. It depends on the context whether the two can be used interchangably or not. And I feel that in this very context both упрашивать кого-нибудь and упрашивать, чтобы кто-то sound natural. As for me, I would interprete this like " умолять, чтобы ХОТЬ кто-то/кто-нибудь стал моим другом.", though there's no word to emphasise in the English sentence.

We stress it by saying both: "...begging somebody, anybody to be my friend."

Oh, you're right, Uly!

Aleh, здесь не имеется в виду "упасть на колени", потому что "упасть/встать на колени" - это "to get on one's knees". Здесь речь идёт о том, что человек не хочет уподобляться животному (собаке, например), то есть не хочет вставать/опускаться на четвереньки. Если бы речь шла только о коленях, то в оригинале так и было бы написано. Это не идиоматическое выражение, поэтому, на мой взгляд, не нужно его заменять чем-то, что здесь не имеется в виду. Ещё все-таки "to be short of something" - это выражение, означающее, что чего-то не хватает, что человек испытывает недостаток в чём-то (как в прямом, так и в переносном смысле, как здесь).

As for the choice between "кого-нибудь" and "кто-то", I believe that Uly is absolutely right here. You see, in such contexts "кто-то" in Russian usually means somebody you know, while "кто-нибудь" means anybody at all. Here this person means that he has no desire to beg people to become his friends.

And I don't agree with you.In the case above, as in many other situations, кто-то и кто-нибудь can be used interchangeably without any difference in meaning. They may require a different grammar constraction in Russiun, though.
Actually, Olga translated it, as if "anyone", not "someone" was used in the original version.So you contraduct yourself.

Actually, Olga is right. The meaning of "somebody" changes according to whether we stress it or not. When we don't stress it, as in Russian it means someone whose name you're not mentioning or you've forgotten: "Somebody told me you lost your job." - you know who this person is. However (strangely enough) when we stress this word, it acquires the same meaning as ANYBODY, i.e. it doesn't matter who (no specific person in mind). Stressing this word has the same effect as putting хоть in front in Russian. For more emphasis, we add the word ANYBODY afterwards and stress it too: I need help. "Please send me SOMEbody... ANYbody!" So in the original post, the word SOMEBODY would definitely be stressed and thus correspond to хоть кто-нибудь, meaning ANYBODY AT ALL (in the whole world, town, etc.).

Well, I'm not going to argue with you, Aleh. It's just my sense of language tells me that it should be translated the way I did. You by any means may have your own opinion. No biggie :)