Though I'm not sure exactly what the problem may be with your system, the first thing you should do is to try a different memory card in the same slot. If nothing shows up, you know it is the system and not the card (still, it could be hardware or software). You could also put the same memory card into slot 2, see if that works. If it doesn't, put a different card into slot 2 and see if that works. Also, though this is going a far way, you should try your memory card on a friend's PS2 - one that works perfectly.
How old is your PS2? These things breakdown after a while!