Now we are getting somewhere! The broken traveler cover could indicate — likely it does — that the shift cable is either binding (not likely) or stretched so far that it isn’t even working. So, what is happening is that you are hearing clicks as the shifter goes through the gates, where everything stops.
If you have access to the right tools and feel comfortable doing this, I would suggest that you park your car on a flat or level surface and set the parking brake. Once you have the brake set, I’d get inside the gearshift console and access the gearshift adjuster cable. It should be at the end of the cable with the sheat. At the same place, you will find a nut with a steel wire running through it. This is the gearshift cable and adjustment net.
Loosen the adjustment nut a bit — only until you can move the steel cable easily. Then, using a Vice Grip (R) style pliers, first pull the cable until it tightens somewhat in the carrier (sheath). Don’t pull it very tight or you risk damaging things. Once it is tighter, tighten up the nut and try shifting your vehicle (don’t forget to press the clutch). I think you will find things starting to work a bit better, although the fact that the outer sheath is also broken does alarm me. It may indicate that the entire gearshift cable/adjuster assembly is broken and has to be replaced. This could easily account for the way your tranny is acting. Though it is not a hugely expensive repair — $350 or so with labor — it is important that everything is set up as it is supposed to be or else your transmission won’t work, no matter what you do.
After it is fixed — I’d let a technician do this as it involves attaching the carrier and then threading the cable correctly to each gear — try starting up, with the parking brake set so the vehicle won’t move. I’ll bet that your Vibe will now stall — which is what it should be doing.