The problem sounds like a wiring fault to me. Landlines ring when the POTS (plain old telephone system) provides power on the receive wire. See https://www.lanshack.com/wire_phone_jack.aspx
for the RJ-11 wiring diagram.
Try a different phone at the jack and a different telephone cord. If it rings constantly, that tells you the problem is with the wiring in the building or outside. You need to find where additional electricity is coming into the telephone wiring. Check the jack first. Most jacks either have screw terminals or keystones. Use the wiring diagram above to make sure that the wires are connected to the correct point. If you have the screw type of terminal, you need to strip the insulation from the conductors before securing the wires. For the keystones, leave the insulation intact. Then use a punch-down tool (available at most hardware stores in the electrical section) to push the wire into the correct slot in the keystone.
There must be a place where the insulation is damaged and touching another wire or water is in contact with bare metal and a current is flowing across the water. If only the Uniden phone rings constantly even with the new RJ-11 cable, replace the phone.
I hope this helps.