I am also having some trouble picturing what you are doing car jumper leads. I am guessing that TD is right about the jack having failed. I'd love to have a pic of what you are doing with the jumper leads.

A word of caution before anything else. While a solid state amp may not have the really lethal voltages that a tube amp has, it can still give you a nasty shock or do damage to internal components if you don't know what you are doing. This is even true when it is unplugged. There are some folks on the board that know what they are doing (WeirdBits, DocNomis, Simon) but I am not one of them. For my part I typically won't service my own amp, unless it is something very easy, and very accessible. This might qualify as such, but if anything makes you nervous, consider taking it to an amp tech.

On an old amp, the jack would look a lot like the one on your guitar. Those are relatively easy and straightforward to replace. On an amp made in the last...maybe 20 years?...it's probably mostly on a circuit board, and that includes your Line 6. I googled it, and there may be some variations depending on the time of issue, but I think it will have an input jack that looks a bit like this:

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If so you won't be able to see the tip-connector, because it's inside a housing and not meant to be disassembled. The good news is that if it's easy to get to it should be easy to replace. Here's a video of a guy doing it: