Why won't he ask me out?

We need an overt sign that you're interested romantically and that you're not just being friendly. It's common for women to flirt yet have no real interest in dating us.

After experiencing this for a number of years, many guys get "gun-shy" and lack the confidence to make the first move.

First, are you sure he's unattached? If he's married, he might be afraid to get involved with someone so close to home (i.e., maybe he knows people on the train who know his wife, too). If a guy is going to cheat, he'll tend to find women far away so he can live a double-life.

Second, he (or his family) might have certain essential "criteria." For example, some Jewish guys will only date Jewish girls. Assuming you pass these sorts of tests, the next time you see him, I'd advise you to look at him with a loving pair of eyes. Eventually, you'll break down his resistance with a killer romantic gaze.