V + 을래야... 을 수가 없다 is part of a structure that says you tried or intended to do something but did not succeed for some reason. Commonly found in speaking, the full pattern is:
너무 시끄러워서 잠이 들을래야 잠이 들 수가 없었어요. It was too noisy so I tried to fall asleep but couldn't.
열차가 가득해서 자리에 앉을래야 앉을 수가 없었어요. The train was crammed so though I wanted to sit down but couldn't.
음식이 너무 짜서 먹을래야 먹을 수가 없었어요. The food was too salty so when I tried to eat it I couldn't.
마지막 버스를 놓쳐서 친구랑 만날래야 만날 수가 없었어요. I wanted to meet my friend but I couldn't because I missed the last bus.