Update: I've opened up the PS3 and noticed that the Bluray drive is working fine mechanically. I've even opened it up and cleaned the laser. I've also powered it on and confirmed that the disc does spin, but stops shortly after. Maybe it stops because it can't read the discs. I've also tried doing a factory reset of my PS3.
Are there any other things I can try to get this to work? I was reminded how expensive the PS3 is, and am not looking forward to buying a new one especially with the PS4 around the corner.