You can check for reset by inserting a sign-on message above your main program loop.

LCDOut $FE,1,"Start"
PAUSE 2000 ' Display sign-on message to 2S

Loop:
Main program starts here

You only see the Start message on power-up or hardware reset.

If you keep seeing the sign-on message, you know there's a problem.

Disconnect RE2 from your LCD W pin, and connect the LCD's W pin directly to ground. Comment out this line (Low PORTE.2)

Now comment out the A/D part, and just loop through displaying messages on the LCD. Does it work?