When you use sprites it actually uses a 3D plane so the blue backdrop always clears the screen... any 2D drawing commands won't be seen because the screen is cleared automatically. You just need to grab that newly stretched background as an image and paste it to the screen every loop.
` Sync as fast as the computer can handle it
sync rate 0
` Turn on sync
sync on
` Load the bitmap
load bitmap "BackTest.png",1
` Copy the bitmap to the main screen (bitmap 0)
copy bitmap 1,0,0,bitmap width(1),bitmap height(1),0,0,0,screen width(),screen height()
` Change focus to the main screen
set current bitmap 0
` Get rid of old bitmap (don't need it anymore)
delete bitmap 1
` Grab the new background (so the resolution change is saved)
get image 1,0,0,screen width(),screen height()
` Make and grab a small image (for the sprite)
ink rgb(0,255,0),0
box 0,0,50,50
get image 2,0,0,50,50,1
` Hide the mouse
hide mouse
do
` Show the background
paste image 1,0,0
` Show the sprite at the mouse coordinates
sprite 1,mousex(),mousey(),2
` Update the screen
sync
loop