it doesn't jump from the solenoid, it just clicks. I am actually wondering if I fried the grounding wire, I could smell a hint of burnt wire.
I thinking your battery is no longer to deliver it's full rated CCA amperage. Repeated deep discharge and over charging at too high an amperage, jump starting from a running automobile can damage these little batteries and cause the battery to loose capacity. Have the battery load tested, about any auto parts store can do this to see if its delivering its full rated output. If weak replace, it may be just too far discharged, charge overnight with a 2 amp charger. It takes a minimum of 10 hours to fully charge a discharged 20 amp/hour battery at 2 amp rate.
By jumping across the solenoid what is meant is to use a pair of old pliers or two old screwdrivers to physically short the two large terminals together at the solenoid thus giving the starter a direct path to the battery through what ever you are using to jump out the terminals with. If it turns over good then the problem is with the solenoid, if it still doesn't then its either the Battery, or Wiring connections at the battery, Large wiring connections at solenoid, Starter connection, or main engine ground loose or corroded or Perhaps a bad starter. What you are smelling are the contacts burning and ozone from the arcing of the contacts as they start to open from low voltage. The smell does not necessary mean your solenoid is fried or bad.
The solenoid is just a relay or switch that via the push button supplies to a low current signal to energize a coil that causes large high current contacts to connect the two large wires together internally. In actuality, both large wires are positive. One is hot all the time the other is hot only when the solenoid is energized feeding power to the starter. There are 3 small wires, Black is a coil ground, green is coil positive which momentary supplies 12 volts from the push button to energize the coil. and Red is 12 volt supply from the battery to the fuse box which is internally connected inside the solenoid to the large positive cable connection from the battery.
The clicking is caused when the voltage drops below the level needed to energize the solenoid coil. The starter takes a lot of power or juice and places a lot of load upon the battery. It can cause the battery voltage to sag below the level needed to energize the coil. Then the coil looses power and the solenoid opens, since now there is no load on the battery, voltage recovers high enough until enough to re-energize the coil and this starts all over again, click, click click as the main solenoid contacts make and break with high and low voltage from the battery.. Weak bad battery, Battery not fully charged, Loose cables or bad starter is always the problem in such cases. If you were to look at the battery voltage while the solenoid is clicking, it would be jumping from about 7-9 volts to almost 12 volts as the solenoid contacts clicks open and closed.
In rare cases the main high current contacts of the solenoid could be pitted or corroded enough to prevent full current from passing through them to the starter. This would not necessary cause a clicking sound, just appear like a weak battery or not enough power to turn over the engine.
Remember all of his, so you can help out the next guy that posts a problem with a clicking solenoid and I'll not have to retype all this again. <grin>