I’m trying to remember the name of a singer I saw once on David Letterman back in the late 80s… her name started with an H… possibly Ha… anyway she sang sort of Eastern (India/Arabic) type music. I remember finding her in the pop section of the music store at the time. Who is it??
Ofra Haza? (Israeli singer of the 1980s and 1990s, sampled by Eric B & Rakim and MARRS, died last February?)
YES! That is it! Thank you thank you thank you! Oh man, she died? 
AIDS-related complications, unfortunately.
I still remember “Im Nin’alu” (IIRC) making the charts here.
From the title, I’d guess you are looking for Bill T. Kat, lead singer for Billy and the Boingers. Alas, Mr. Kat has faded back into the obscurity from whence he came, after a scandal involving the bands Tuba Player, Jeanne KirkPatrick(sp) and two tonnes of Atlantic Herring.