First, your mechanic pool is to be pitied.

Don't go to a carb, the FI on an 83 Vanagon is a fine, and fairly simple
system.  To me it sounds like the culprit is more likely still your
starter.  While it may crank the engine over fine, your FI needs something
like 9 volts to run it, and if your starter is dragging the battery below
this, then it would go a *long* way towards explaining your troubles.  A
short on the heater switch lends credence to this remote evaluation -- no
start because the voltage at the FI computer is too low.

Is this a manual trans?  If so, try push starting it.  If the problem is
low voltage due to the starter, it should push-start easily.  If it is an
automatic, well you can't really do this test.  Also take your voltmeter
(buy one at Radio Shack if you don't have one!) and look at the voltage
available when you crank your engine.  You can buy a cigarette-lighter plug
and wire it into the voltmeter.  It will be handy in the future.  If this 
voltage is low, start looking to be your own mechanic.  Any mechanic that
won't even look at your FI is not a good one.  A carb will never run well
enough to pass smog on an 83, and you'll be lucky if you're happy with one
regardless.

Clean the contacts on all of the FI plugs, including the many ground
connections.  Even if your battery offers up 12 volts, the resistance in
a slightly corroded connector can drop the effective voltage enought to
cause this.  As many VW bus owners have found, poor connections are more
often a source of troubles than all other things combined.  Usually they
find this out after replacing many components for many, many dollars.

malcolm