Escape Won't Starr

My 2002 Ford Escape (xlt v6) won't start. I
have a brand new battery and all lights
are working. It just won't start at all. It
doesn't make a sound. I had this issue the
other day. Once I jiggled the shifter and
stepped on the brake, it started right up.
That trick isn't working much anymore,
sadly. I also noticed that all the gears are
lit up, like the truck doesn't know what
gear I'm in. It drives fine (when it starts).
Is this a starter issue? Solenoid? Any help
is appreciated. Thank you!