I had no problem at all installing 3.7.4 on a shared hosting account. I just entered my user/password for MySQL and later got to chose which DB (of the ones I had access to) should be used.
Did you try just simply entering your "normal" priviledged user?
However: PHP 4.4.1 was a horribly broken release (4.4.0 and 4.4.2 are ok) and maybe you're having trouble with that, really.