I agree it is most likely the light that is the problem. The Aqueon tube is very low intensity, I had one that came with my 29g tank (a 17w 24-inch tube) and it went out to recycling the next day.
Unfortunately you are going to have to go with one of the more expensive fish-store tubes here. I bought a GE Daylight for my tank, and it is not sufficient light. The Life-Glo that I had was much brighter, and the plants managed then.
I would get a Life-Glo, or an UltraSun by ZooMed which is basically the same but a bit cheaper (here anyway). Another option i don't normally suggest is the Power-Glo, also quite expensive but it does put out a bit more light; it has a purplish hue which i don't like, but if you are used to the Aqueon (it is similar in this respect) you might not find it odd.
Not sure it would be that much better over the Life-Glo or UltraSun though, to be honest.
This is the tank where a single T5 HO tube would be ideal. I'm thinking i should try to track one down for my 29g, meaning a new light fixture in T5. Even with a good tube like those suggested, I find the plants are just managing, sort of.