What CD burning software do you use other than WMP? That'll make MP3's/WMA's but it won't burn to disc in a playable format (I may be wrong) that a CD player can read. The convertor probably wouldn't work either, as the disc itself has to be specially encoded to boot up on a CD player, which simply placing CDA files on a CD wouldn't do.
I'd try getting Nero if I were you. It can quickly make audio CD's with a press of a button