What does Verizon claim they will deliver? If they are charging for higher speeds you should be getting higher speeds. That doesn't mean Verizon is at fault, but to answer this question we need to start there. Verizon is difficult to deal with, but they should be able to
tell you what they mean when they say the signal to your point of entry
is good. How good is good? What does their testing indicate in terms of
how much speed you should expect?
How far are you from Verizon's central office? They should be able to tell you that. Distance matters.
What is your interior wiring like? if you're on old low-grade phone wires you may have so much noise in your system that you'll never get full speeds. Can you work on your wiring? If so, you might want to think about adding a data-quality line (CAT5) to the modem.
Is a land line phone on the same system as your DSL? If so, do you have adequate splitter/filters on the phone lines. This is essential to getting full speeds.
I think it's unlikely that your router is the primary limiting factor in
your DSL speed. A three year old router should be fully
functional. What kind of router? Can you get a router stats page on the
router software? You should be able to get a noise margin or
signal-to-noise reading. That will tell you a lot.
My best guess, based on the limited information you provide: Your interior wiring is not up to what it should be, either the quality of the lines or the appropriate splitter filters on the land line phones. You need to find out where your limiting factor is. The modem or router is not the likeliest first place even if it is the easiest to deal with.
I've had a DSL modem plus wireless router for Verizon for a couple of years and have been unsatisfied with its speed. Hulu hangs up and computers in the house often show only a 1Mbps connection. Should I be thinking about replacing the modem?