I have a question about "tongues"

This time I've got a question for folks reading this. So far I haven't found any good source of information, although I haven't exhausted all possibilities.

The question is: What Biblical support is there for the "prayer language" form of "tongues?"

First, let me tell you what I've heard and don't find adequate.

The biggest support I've heard is found in 1 Corinthians 13:1: "If I speak in the tongues of men and of angels, but have not love, I am only a resounding gone or a clanging cymbal." (emphasis mine) The phrase bridges a discourse Paul gives about spiritual gifts, specifically speaking in tongues or unknown languages, and the famous definition of love. The Corinthian church had focused all too heavily on the spiritual gifts (not to mention following the teachings of men), and not enough on Christ.

The problem I have with using this as "proof" of the gift of tongues including a private "prayer language" that does not correspond to any existing language (and, therefore, does not require an interpreter, as seen in 1 Corinthians 12) is that the notion of "tongues of angels" just pops up out of the clear blue, and really isn't supported elsewhere in context. I see this as more of a form of exaggeration, as though Paul is saying, "hey, look. I don't care what you think about speaking in languages you haven't learned. That's not important. Even if somebody were to claim to speak some language direct from Heaven, if that person doesn't have love, it's no good!"

I've also heard all the supposition about the "unknown prayer language" being a sort of "code" between your spirit and the Holy Spirit that allows communication that Satan cannot intercept or interpret. Sorry, but if Satan was one of the highest angels who still has free contact with God (as seen in the book of Job), I cannot see how this is supported by Scripture. Even if Satan does hear our prayers, God is greater and still in charge ... who cares if he hears or not?

Sometimes peole will refer to this "prayer language" as being the "groanings that cannot be uttered" mentioned in Romans 8:26. Sorry, but what I hear referred to as "prayer language" has more sounds than mere groans. Besides, prayer language is uttered, or spoken.

For the record, I do accept the notion of speaking in tongues, and the interpretation thereof. I witnessed one lady doing this, and while I could not interpret, I did recognize a grammatical structure. I also accept the story, published in Guideposts several years ago, about the woman who ministered to a German widow, all the time speaking and hearing German, even though she did not know German, nor realized she was doing it at the time. Although I've studied French, it came to me fairly quickly, and I can still hold my own, even when out of practice (although my vocabulary fails at times ... as I tell people, "je me souviens un peu des mots Français"). I do not accept the notion that one is not saved or has the Holy Spirit dwelling within them unless they "speak in tongues" of either type.

I would appreciate any references folks can supply.