Can I use my electric coffee pot on the stove?

It would help if you had posted some pictures. In any case i would NEVER use an electric appliace on the stove top.

A quick search in ebay for "corning ware coffee cable" yields several results.

Not a good idea. Electronic kettles usually contain PVC or other plastic parts in the electronics. During normal operation, the heating element might be located far enough away or insulated from the plastic parts, but on the stovetop that insulating strategy will likely be ineffective. Never use electronic cookware on the stove unless product documentation specifically states support for that use case.

No

Do not put your electric coffee pot on the stove, it is not made to conduct heat applied from outside to the inside of the appliance. Additionally, depending on the type of stove, you risk burning several parts of it, like the cable or what appears to be a coating of sorts on the outside.