The problem is almost definitely your neutral safety switch. When you jump the solenoid you are bypassing it.
The problem is your starter is going and needs replacement
If the vehicle has an automatic transmission, then the torque converter clutch is probably sticking. The clutch is controlled by a solenoid, that moves it back and fourth. The clutch material can get stuck to the inside of the converter and stall the engine. Have the transmission flushed, and if the problem persists, then have the solenoid replaced.
make sure the small wire is hook to the post
If you have code P1776 solenoid switch valve latched in low/rev position. You have a sticking valve in the transmission valve body. The valve body will need cleaned/replaced.
It is not repairable and should be replaced.
The wire from the battery to solenoid is corroded & should be replaced.
may be on top of the starter and replaced with same. Follow the + battery cable it will connect to the solenoid
If you replaced the correct shift solenoid (SS B), check for a broken band in the trans.
The starter solenoid can be replaced by removing the wiring harness. Remove the retaining nuts. The solenoid will come off. Reverse the process to install the new solenoid.
The solenoid pack on a Chrysler Sebring is on the bottom of the transmission. It is a bolt on unit and can be easily replaced.
Your solonoid needs replacing. Solenoid.
It will cost approximately $60 to replace a solenoid in your Ford Explorer. The exact cost is dependent upon which solenoid is to be replaced.
Solenoid switch valve latched in the low/reverse position. On a 300M it is usually a failed transmission solenoid pack.Solenoid switch valve latched in the low/reverse position. On a 300M it is usually a failed transmission solenoid pack.