Mitsubishi WD-62525 Input 480i

Replace service cords, as they might be getting worn and loose. It does sound like that to me. Bad coaxial cables

http://www.retrevo.com/support/Mitsubishi-WD-62525-TVs-manual/id/276ag909/t/2/
http://www.techlore.com/download/25244/Mitsubishi-Service-Manual-WD-52525-62525-52725-62725-52825-62825/
Ok top user manual, below a service manual, this will help you troubleshoot and possibly repair.

how long does the set run before you get the message?

Your tv would turn on if you replace the only two 3300µf@16v capacitors on the power board . You wil notice they are bad by the way they bulge up at the top and may be leaking electrolyte a little from the tops . But the rolling lines would still remain but much less noticable.Then other symptoms will eventually appear. Truth is many many many many other capacitors need to be replaced inside the electrical chassis. Your TV would need to go to a repair shop that is expierienced in that repair because it is so extensive.

You will have to use component inputs for above 480i, and use the FORMAT key on your remote control unit (lower panel in center) to change to whatever you want for resolution. Be sure you have your signal input set to one of the Component inputs via Setup or Net Command (or use Devices on the remote)

You have lost the input signal...you will have to go to Setup/Net Command and set your input to the one with signal (either a TV input or a Component input). If it is reset...the input likely switched to a non-usable input

It has been renamed.

I would lean towards the main board

Since the set turns on and displays this message we can asume the set is working, so for the next step simply change inputs and see if something comes up, either there is nothing hooked to input 1 or the device hooked to input 1 is off or has failed

Mitsubishi list this problem and has a solution of replacing several small surface mounted caps and diodes. we have tried this repair 5 times and only successfully done it once. so replacing what is called the formatter board part # 930B924002 for around $ 350.00 usually repairs this type of failure, However changing this board is a time consuming thing and takes a lot of Patience. It is buried deep in the set and several other board have to be removed just to get to it