Line 2 is engaging but not working.

Do you have a single line phone that you can use to test that line 1 and line 2 work independently with the 86109 disconnected?

Are these traditional landlines or digital that plug into a modem? Straight line phone as suggested by @JefferMC it the best way to check individual lines. If this is digital service reset the modem, if traditional landlines sounds like you're working on split pairs. 

  Good suggestion. With the unit disconnected from the lines, Line 1 continues to ring, line 2 provides the line not working warning. I take it that this suggests that the problem has to do with the actual incoming line?

Please explain how you're testing to get that information. 

Unplugged base from incoming line and power. Dialed line 1 ( rang no answer) dialed line 2 ( warning).

OK, you dialed line one from what and did you try to answer it? I don't know what dialed line 2 warning means. You have to be clear so we can try to analyze the issue. To be clear, plug a regular plain phone into line one, call it from a cell phone or whatever means you have. Does the phone ring and can you answer it? Or do you just hear audible ring on the device your calling on but the line never rings? Next plug the phone into line two, do you get dial tone and can you call out? Can you call and answer line two? If neither line works and you can test from the NID do the same test at the NID and if neither line works, or even if just one line doesn't work from the NID, report it to the phone company. Still need to know what your service is. 

 Called land line 1 from a cell phone with land line unit with no power and no line connection. Cell phone hears unanswered ringing.

 Called land line 2 from a cell phone with land line unit with no power and no line connection. Cell phone hears warning of your call cannot be answered.

 If land line unit is powered and line 1 is called from a non connected phone ( cell, land), line 1 will ring and you can communicate with it. At the time that you pick up the receiver line 2 indicator will illuminate. If you place line 1 on hold and answer line 2 there is dead air.

If land line unit is powered and line 2 is called from a non connected phone ( cell, land), line 2 indication on the unit will not illuminate and the exterior phone will hear the warning that your call cannot be answered.

Report it.