Appreciate you asking, Terry.
Without directly having your modem in front of me, I'll have to surmise that Electrolytic Capacitors inside the modem have gone bad.
These capacitors are used as Filters.
After a given time they break down. In fact the designer knows this, and uses capacitors that are 50 percent better than what is required.
One wouldn't think that within a two year span the unit would breakdown, but there are many variables that can add to their demise.
1) Power outages
2) Dirty inside, (Use a can of compressed air in the vent holes occasionally. There is no fan inside, and air is used to cool the components inside. Unit UNPLUGGED from power)
3) Low quality components used inside the modem. Especially Electrolytic Capacitors.
My recommendation would be along the same as yours.
Buy a new modem.
You didn't state the Model Number, so I don't know if it is a wireless unit, or not, nor do I know if it is a cable unit.
Wireless, of course will be more expensive.
A couple of recommendations from a quick search.
Not advertising for said website, nor manufacturer,
A visual guide to bad 'caps',http://www.capacitorlab.com/visible-failures/index.htm
Should you have any further questions please do not hesitate to ask. Post in a Comment.