Car runs good, but 10ish minutes into driving my transmission will not engage, but when I turn my engine off and on again it will drive.

it’s an auto trans (I know) but I’m really screwed and need my car to be running

I grabbed a new trans solenoid from the junk yard didn’t fix the problem

fluid level is good.
100k miles on tranny

 

Fluid level ok? Condition?

 

Fluid level is good
and by condition I assume you mean miles?
100k
looks clean shifts nice in the higher gears does a little kick from 2-3

 

They mean the condition of the fluid. If the fluid level is fine and it isn't filled with metal particles or smells/looks like it caught on fire at some point it's probably fine. It might be worth servicing the fluid though, how long ago was last trans fluid change?

After fluid level and condition has been addressed, the next thing to check would be the linkage. The auto will have a throttle valve cable/linkage that might need an adjustment or cleaning. My manual actually has a note about the throttle linkage appearing to function when the engine is cold, even though it malfunctions at normal operating temperature. Hopefully that is what's going on here, as it is a simple fix.