You do apparently need a Playstation 1 memory card inserted into a playstation 2 to play PS1 games,
but it sounds more like your lense is struggling.
Try a memory card first (1MB card for PS1, not a 8MB PS2 card) but failing that use a lense cleaner, and if that fails, try manual cleaning of the lense CAREFULLY with a cottonbud and some isopropryll alcohol (video head cleaner fluid) just dont put lots on and make sure its evaporated before powering up the unit.
Most PS2 lenses don't clean with lense cleaner discs but do come back to life with manual cleaning.
If you smoke, you can be sure it is the lense, as nicotine and tar cover laser lenses with a mysty glare which you can see by trying to reflect daylight off it.