Would you seriously want to be in a proper relationship with a man who will guiltlessly cheat on his girlfriend for so long?
Think about what it's like for her. What would it be like if he got rid of her, got together with you, and then started boning someone else? Remember that quote "When a man marries his mistress, all he does is create a vacancy".
(Also, it may be wishful thinking on your that they're not getting along well - he might be avoiding talking about it because he doesn't want to bring it up with you around rather than because things with them are crap, and not going out anywhere together when they doesn't mean that they're not enjoying each other's company - in fact, if you haven't seen someone for ages, wouldn't you want to just spend time with them rather than being distracted by a film or a play or whatever?)
My advice for you is get the hell out of there. He's a cheat. And he should come clean with his girlfriend.