Thanks Sliat. Yeah, those songs would be nice. Before you search them, though, please check these links and tell me if they are the sames that you have.
Cutey Honey (from New Cutey Honey)[Takeo Watanabe, Keiko Nakida] (
http://sharebee.com/0b8d8758)
Shin Cutey Honey Op - Vocal (
http://sharebee.com/a0062fab)
Shin Cutey Honey - English Opening (
http://sharebee.com/5f4c3c56)
New Cutey Honey - Ending (
http://sharebee.com/e8a5c2f7)
"Shin Cutey Honey Op - Vocal" comes from this album:

(
http://img340.imageshack.us/my.php?image=cocc12543frontoe1.jpg)
(Unfortunately, this album didn't have the songs I'm seeking like "Burning Up!", "Legend of Good-Bye" or that particular intro I'm looking for). I got these songs from different sources, so I do not know what album they belong to (except for "Shin Cutey Honey Op - Vocal")
I wouldn't like to make you lose your time searching for these songs. But, if you feel like it, please upload them all, since the ones I have aren't particulary high quality (128kbps).
According to ANN, these are the ending and opening themes:
Opening:
"Cutey Honey" by les 5-4-3-2-1 (eps 1-4)
"Cutey Honey (English Version)" by Mayukiss (eps 5-8)
Ending:
"Circle Game" by les 5-4-3-2-1 (eps 1-2)
"Rendez-vous in Space" by les 5-4-3-2-1 (ep 3)
"Legend of Good-Bye" by Mayuki Hiramatsu (eps 5-8)
It's quite possible that all these are the ones in the Cutie Honey Song Collection Special. I'm guessing, but I'm not sure, that the theme from les 5-4-3-2-1 is the one I'm looking for, since it seems I don't have it yet. Does it sound the same as the English one? It's more than enough for me if I can find that elusive opening and "Legend of Good-Bye". I can't believe that opening wasn't included in the DVD's or any releases other than the original VHS. There are a lot of versions of the Cutey Honey theme, which makes really hard to find the one I'm looking for. But once I've heard them, I recognize them easily. The "Onegai" part it's quite distinctive for every singer. That's how I know, none of these themes that I've uploaded is the one I'm dying to hear again. Besides, the music should sound the same as the English version, which, as you'd be able to listen, none of these does.
Other than the vocal songs, I'm also looking for an specific background music. It's the one played after Honey pierces Dolmeck's armor (
http://www.youtube.com/watch?v=fE2mZ8gctps). But I know quite well that'd be almost impossible to find, so I'll have to learn how to rip music from a video.
PS. Sorry for writing too much.