It's a Homalonema.

Thanks for the input. Now I know, after all this time, what kind of plant I have. I guess it's kind of sad that I've waited this long to try to learn about it. Better late than never, I suppose.
I have to say, it's been a tough plant. And now I know why I've never seen blooms. After some Googling, I'm thinking this may be an 'Emerald Gem'. Looks like they are grown for foliage. Those 'shoots' that I'd seen in the past were probably the extent of the blooms that this plant will produce. I was hoping for a showy spathe, like an anthurium. But this is a nice plant and it is special to me, as it was from my Dad's funeral. I take it that these things are rather long lived since I've now had it for over 10 years.

I guess my only remaining question is what to do about this:

{{gwi:385955}}

Should I divide that part from the rest of the plant and replant it deeper so that the brown part is below the soil? Then, I imagine the roots will be even further down. Is that a problem?

Thanks again for the help.

Its not a "problem", its just a natural way some aroids grow over time. Some eventually form trunks.

OK, I had no idea. The only thing is that it gets a little floppy when it's like that. I guess I can always stake it if need be.
Thanks for letting me know.