Thanks to all who offered advice and suggestions. I finally got it lit last night and left it on until now. This morning I filled the small tray from the freezer with water, and tonight the tray was frozen solid. I take that as a good sign. I buttoned everything back up this evening (bad weather coming in), but I hope to take the burner, etc. apart this weekend and clean everything well, following the instructions in the manual.
Thanks again. If I can get it to stay lit with the flame door closed, maybe I won't have to replace it just yet. :)