Sorry for the late response. Was out on vacation.
The game is Twinkle Star Sprites, JPN. It is a direct rip of retail copy.
The good news is that I tried the game on my brother's slim PS2, model number: SCPH-77001 and it works great.
The discs are Sony DVD+R, and my conclusion is that perhaps my fat PS2 which is version 1 has a laser that is either recognizing the disc with ESR mode, or it has something to deal with mechacon.
Nonetheless, thanks to everyone for your help. Fat PS2 I will use swap magic as necessary, and slim PS2 I will use ESR.