Shop blew my transfer case a F Differential

Drive train engineering question...I have a
2011 Tahoe z71 4x4 ,  I had some to have my
transmission rebuilt. The shop test drove it
after putting it back together. The drained my
transfer case but did not put fluid back in
before the drive. They call me and say, $600
more to rebuild the transfer case. I came into
the shop to see the gears and clutches of the
transfer case, they were blackened, but had
new yellowish fluid all over them.They call me
back 2 days later and say my front differential
is locked up. I did not have these problems
before their test drive. here is my question...
while they test drove my vehicle in 4 wheel
drive with a dry transfer case they Burt the
case gears up, how could this affect the front
differential locking it up ? I took my Tahoe to
another shop to have a used one installed
$1,300.00 more. Please contact me back
with a drive train specialist, I have a court
date 8/15/19 with the shop owner