Could be timing chain.

The other night my olds with a 3800 series II with 176000 miles started
missing(skipping)  badly, no metal to metal noises or overheating.  I was
almost home and so decided to continue on since I figured it was time again
for plugs and wires.    I later tried to start it and the starter would not
turn the engine.  After having had multiple things go wrong at the same time
on cars in the past I thought to remove the starter and have it checked,
nothing wrong with it or the battery.  Since then I have tried to start it
repeatedly and have gotten the starter to turn the engine, although slowly
and with the sound of soft backfiring.  So tell me, does this sound like a
timing issue or what?  If so, how much damage am I looking at.  Would it be
cheaper to replace the engine with another used engine.  I have found an
entire drivable parts car that is a '91 Eighty eight.  
Would that 3800 work in my car, if so, what trade offs and adaptions am I
looking at.  I really like my car, and I do not like anything out there
enough to spend what the price tags asks.  I drive rentals all the time with
my job and I have yet to drive anything in the last 5 years I would consider
making payments on.