Primary source for composer info:
http://bsm11084.hp.infoseek.co.jp/fumei.html
More detailed info about artists:
The original Street Fighter (Fighter Street is the name of the PC-Engine port) was composed by Yoshihiro Sakaguchi. I haven't found who arranged the music for the PC-Engine, although.
http://en.wikipedia.org/wiki/Street_Fighter_(video_game)
Monster Lair (aka Wonder Boy III) music was composed originally by Shinichi Sakamoto and arranged by Jun Chikuma in the PC-Engine port.
http://www.arab-music.com/bomberman/
It's universally known that Ryo Yonemitsu took charge of the arrangement of the Ys series in the PC-Engine games.
However, I have my doubts about who did the music for Gambler Jiko Chuushinha (ぎゅわんぶらあ自己中心派). In many sites the music composition is attributed to Mecano Associates, but the first site I've linked says that Hudson (ハドソン) did the music. Possibly someone from Hudson arranged the music composed by Mecano's composers, but I don't have proofs for confirming it.