My model BL 102-4 phone cant be answered. It just keeps ringing

Have you tried plugging a known working corded phone into the modem? You say you have AT&T Internet, but is your digital phone service from AT&T?

I have another phone that works just fine. I use VOIP, but that is not the problem either. 

If one phone works and another doesn't than it's the phone that doesn't work. Have you check the ringer settings? If all setting are good then the phone system may have gone bad. I'm reading your problem as only the BL102-4 cordless system doesn't work. If other phones are plugged in to instead of the BL102-4 they work fine. 

So I should assume the set I purchased 6  months ago is useless. I know others have had the same problem. I have yet to read a solution. I was hoping for one here. 

If the VoIP service you're using isn't seeing the off hook from your phone system, there's not much you can do. Have you tried resetting the ATA if your phone service isn't AT&T, you're being a bit vague about that. Also you don't say if it works ok calling out. 

I am really looking for someone who has the same phone, with the same problem who can say, do this, do that and fix the problem.