The fax machine can't detect a dial tone (from a POST line). Since the Pixma MX420 doesn't have a handset, you may need another telephone to check your line. First, make sure that the telephone cord to the wall jack is connected to the RJ-11 port marked L. This is the lower of the two ports on the all-in-one printer. If the cord is in the wrong spot, swap the connection. That could solve the issue. If you have a telephone plugged into the upper RJ-11 port, check if you hear a dial tone. (Connect your test phone here if you haven't had one connected and check for the dial tone.)
Next, unplug the RJ-11 line cord and plug it directly into your test phone. Do you hear a dial tone? If you do not hear a dial tone, try a different RJ-11 cable. If the problem is solved, connect this cord to the lower port on the MX420 and see if the fax continues to give the "offline" message. If you still have no dial tone, take your test phone to another jack and try again. Find your incoming phone service box and check if that has a RJ-11 jack. If it does, you can test for a dial tone there. If the box doesn't have a RJ-11 port, you can have your telephone provider check the service.
If there is no dial tone at the service box, then your telephone company will fix the external problem for free. (With copper telephone service, sometimes rodents damage the wires. The provider has to fix this.) If you had a dial tone at the service box or another jack, then you have an internal wiring problem. This could be at the jack or inside a wall. If you take off the outlet cover, you'll find the wiring for the jack. This will either have screws holding down the stripped ends of the conductor wires or a punch-down keystone (with un-stripped wires). For the jack with the screw terminals, determine if any wire is loose/broken and strip a new section of wire. Then re-secure the wire under the correct screw. See http://www.lanshack.com/wire_phone_jack.aspx
for a diagram. For the punch-down keystone, you'll need a special tool to reconnect the conductor wire. This tool is available at most hardware stores in the electrical wiring section.
If the problem isn't at a jack, you'll have to try to find the broken wire and replace the wire. Your telephone company's service technician will fix the problem for a fee.
If you have an internet connection with a DSL filter, you should check if the filter is damaged. This can lead to the above problems. If you have switched to a VOIP service, you'll need to make sure that it is compatible with the POST connection for the fax machine.
I hope this helps.