I cannot know what you mean by "abuts the solonoid". If you mean that the wire has broken off where it enters the solonoid then perhaps it can be soldered if there is any kind of a wire stub coming out of the solonoid. If not then your best bet is to replace the solonoid, new or used, your choice.

The solonoid must be energized to allow shifting up to overdrive (4th gear), running without it working will only allow shifting up to 3rd gear. Some Bricksters have removed the solonoid and cut a fluid bypass channel in it to allow OD all the time. See FAQ for details on this. Also IPD sell a fluid bypass kit that does the same thing. I think their stuff is overpriced.