After months of perfectly normal operation, I started having similar issues about a month ago and have tried most of the fixes reported in this thread (have not manually downloaded and installed drivers, but Device Manager says everything up to date). Microsoft has
contacted me several times and sent a new dock (no success). They called again recently and are talking about sending a new SP3. It doesn't seem like a SP3 hardware problem to me b/c everything works if undocked or if monitor plugged directly into the SP3.
Although still unsatisfactory, here is a work around that works for me: Prior to shut down undock, then shut down while undocked (this is critical), I leave undocked while shut down (don't know if this step is critical if you need to charge while shut down),
start up while undocked (this, again, is critical), when SP3 up and running, dock, the peripheral monitor (set as primary) comes on and all is "well." Of course, still expecting MS to come up with a permanent fix...
03JAN2014: To clarify, my SP3 (i5, 256) will not boot past the Surface logo screen when docked without using the above work around.
18JAN2014: Purchased an "active" mini-display port to VGA adaptor - did not fix the problem. Swapped monitors (both VGA input, DELL 2208WIPI (several years old), DELL 52340Mc (fairly new LED)) - also did not fix the problem. Only work around so far remains: Undock
while SP3 operating, shut down, boot up while undocked, then dock.