You probably have a telephone wiring problem inside your home or your cordless telephone base has failed. I like to use an old corded phone for diagnostics. If you have other phones connected to the same phone line, make sure that all handsets are in standby/on hook.
First, try a different RJ-11 cable between the jack and the base. (Note: I have seen someone use a handset cord here. It doesn't work so make sure that the correct cable is in use.) If the "check tel line" message persists, connect the test phone to the jack with the RJ-11 cable. Do you hear a dial tone? If you do, then the cordless phone base has malfunctioned. If it is under warranty, contact the manufacturer. Otherwise, replace the phone.
If neither phone gets a dial tone, check if the test phone hears a dial tone at another jack on the same line, if you have one. If you have a dial tone here, then you know that the wires in the first jack or between the service box and the jack have a problem. Check the jack. There are two types of jacks: keystone and screw connections. Look for any loose conductors. For a keystone jack, you will need a punch-down tool, available at most hardware stores in the wiring section. Do not strip the wire; just push it back into the correct spot in the keystone. For screw-type jacks, strip the wire and secure it under the correct screw. See http://www.lanshack.com/wire_phone_jack.aspx
for the pattern.
Find your service box. Check if any wires are dangling. I had a service upgrade where the wiring for one jack was left loose behind the siding. Once that wire was connected to the new box, all of the jacks worked. Even though the telephone company said that the service was good, try your test phone if there is an RJ-11 jack in the service box. If you do not have a dial tone, get your phone company to send a technician. The outside wiring needs to be repaired. (Most companies should repair this for free. However, some companies are trying to get more people switched to other service types.)
Do you have a DSL line? If so, where is the DSL filter? If your filter is inside, you may need to replace it. If it is part of the service box, your telephone company technician should fix it for you.
If your phone line has a dial tone at the service box and the problem isn't in the jack, then you may want to hire a professional to fix a wiring problem in the wall. Most telephone companies will provide a technician to do this for a fee.
I hope this helps.
(I have had mice damage copper wire leading to a phone line outage. Other external wiring problems were due to contractors digging too close to the phone line. With a fiber-optic service, when the modem in the service box failed, the phone lost the line and dial tone.)