That is a common problem in 4th gen PS2s. I assume that the PS2 makes clicking sounds when reading discs also? It means the the PS2 is having trouble reading the disc.
Clean the Vice City disc and the lens in the PS2. Do not use a lens cleaning CD to clean the PS2 lens, because I have found that it doesn't do any difference if you do.
To clean the lens you need to open up the PS2 console, and use a cotton bud with alcohol.