Are the phone cables correctly connected to the base unit? Try a new cable for Line 2, if you have separate L1 and L2 jacks. (If the lines are integrated in one jack, make sure to use a 4-conductor RJ11 cord.) I assume the service hasn't been cancelled for line 2 and that you are at a wall plate with both lines.
If you have separate jacks, I like to use a different phone to check the jack. (A simple old fashioned corded, single-line phone is useful to check for a dial tone.) Try checking Line 2 at another jack, if you have one.
If you do not have a dial tone, find where your service comes in. Open the box and look at the terminals. If you are lucky, you have an RJ11 port. Plug in your test phone in to the Line 2 connection and listen for a dial tone. If there is no dial tone, contact your telephone company. They will fix an outside line problem for free. (Mice and other things can damage the wiring. A lightning strike could damage a filter if you use the line for a high-speed internet connection.) If the terminal doesn't have an RJ-11 plug option, you will need to ask your telephone company to test the line.
If you recently had work done on the phone line, check for any wires that are loose. When we got our phone line upgraded to fiber optics, one of the telephone jack lines didn't get connected to the terminal in the new box. We found the wire behind the vinyl siding and got signal as soon as the wire was reconnected.)
If you have a dial tone at the box and no wires are obviously disconnected, you'll need to trace the wires inside to find a broken connection. If one jack worked for Line 2 and another didn't, check inside the wall plate. There are two wall-plate styles. The ones with a keystone jack needs the conductor wires pushed down into the correct slots. A punch-down tool is available from most hardware stores in the wiring section. The screw terminal type requires the individual wires to be stripped and then secured. The correct terminal positions are shown here: http://www.lanshack.com/wire_phone_jack.aspx
. Otherwise, you need to trace the wires in the walls to find the break in the continuity. Your phone company will do this for you for a fee. If you have a line filter inside, try replacing it.
I hope this helps.
(I've called the phone company several times when we lost one line. Mice and lightning damage to the filter have both been culprits.)