Battery fuse blows with key off

this is not clear at all (is 3.4L engine my bet)
the starter is silent or not? if the starter motor spins the enigine crank shaft , fast that that is cranks ok not start engine.
no crank means. the crank shaft never spins
and that as a few causes,
blow fuse test them all?
crank in park and in Neutral too? N can work and P fail on any car.
no power to PCM fuse mean main power is dead main 12vdc power buss is dead. and that is much larger fuse even 100amps.
if you scan the PCM well that action will be dead. lacking PC power
so here is that power feed, battery must be 12.6vdc rested, not 10v
here we go ,2 paths dead, starter motor and PCM dead power.

Fuse link C blow out. GM gray coded,same goes fore Fuse a1/2 blown.
fuse link A, blown GM rust coded make alternator 100%^ dead and now the battery dead too ,lacking working ALT.
next is fuse link Z (GM gray) runs vast things.
I wonder what fuse is this PCM fuse as none are marked that.
there are 100 schematic to see, I am working throught them all to find PCM
are head lamps dead, are brake lamps dead?
head lamps work key off, so is always fix it first if dead.
fuse (Fa1/2 ) PCM/ABS fuse 10amps the a1 side is main power to this fuse. and this also kills dead the transmission range switch PRNDL and starter too dies.
So fuse A1 side is your critical failure point on this car.
so maxi fuse 40amps blew out from a short.
A1 FUSE GOES HOT KEY ON ONLY. (NO IMMO FAILURES IF HAS IT.
IF NOT a ign MAIN 1 FUSE 40AMPS IS BLOW
OR POWER TO MAIN ONE IS GONE.
mIAN1 IS WIRED HARD TO THE BATTERY MAIN
ALL MAXI FUSES ARE, SO IS BLOWN THAT FUSE OR THE KEY SWITCH IS BAD.(IN RUN)

you have a dead short more than likely at that left side blinker ...

Bad alternator or short in alternator wiring. You much need a wiring diagram. Is that the car? Was in an accident? You may have pinched wiring or a wire shorted to ground. Try new fuse with alternator disconnected, then with key on, connect alternator-watch for sparks, or clicks, -you might want to have the alternator tested, just to be sure. You have to start somewhere...
Maybe a wiring short in the blinker system? Or is the fuse blowing an alternator fuse?

if you have just replace a tail light bulb check that it was the right bulb as the problem is a dead short
one bulb type has 2 contacts and the other has 1 contact which if placed in the wrong holder will short out the circuit and blow the fuse

canada or USA, (diffr. laws, different wiring, even DRL up there)
station wagon or NOT?
THE TURNS FUSE BLEW OUT. 2nd time, 3rd,,,?????
that means the circuit is overloaded or shorted.! (prevents fire)
but did it blow a 2nd time, why not say so???

all 4 lamps dead. or stuck on, or flash odd. or what? dim?
does the cluster lamp flash, , in blink or emerg. mode?
wont work , means what, (dead or stuck on or dim)?????
do emergency flashers work? ,dead, stuck on what?
does car drive perfect day or night?
are any other things on car dead, of odd acting?
we see all this , 1st 5 min in a shop, zero here.
ive answered Forenza blinks here, many times.
ever search?

ill now answer by guessing USA non stationwagon and no DRL.
dash box fuse 4 kills blinkers

EF1 (engine fuse) 1 good?
dash fuse 14 and EF1 can kills emerg. flasher

so of Emergancy flash lamps blows fuse 14,(smaller of 2)
then the blinkers are in fact shorted.
does it?
if yes, then find out which side blows the fuse 3.
turns left blow or turns right blows.
so if say turns right blows, F4 fuse.
if true ?remove all bulbs front rear right bulbs.
does the fuse hold now,(means not blown)
then buy new lamps there. problem solved
bulbs can in fact short.
not just blow open.
Tell the full story and all this gets easy.
For sure emergency flash,

the fuse stopped the fire. that is what fuses do.
so, you have a dead short on the blinkers.
remove each lamp 1 at a time.
yes, lamps can short. (twisted too hard)
remove them.
still blow the blinker fuse.?
yes, then the wires are shorted.
and guess what, top reasons are.
1: trailer wiring, look behind each lap assembly, BINGO?
2: hacking or collision, yes, look 1 more time. ,yes behind the lamp assembles, look carefully for DAMAGE.

Recently we had to put a new fuse in the starter ???????????? What fuse ? location , size . A fuse blowing means a electrical short to ground .

Could be grounding out at the starter (bad starter solenoid) Unhook the POS. (large red wire) at the starter and try turning key, see if it blows again. If not, replace starter. I assume you have the battery polarity hooked up correctly? (Red cable to POS on battery, black cable to NEG) Other than that, I would keep looking for a dead short somewhere. Mike

The keys may have to be reprogrammed to the computer (and the fobs, too) at the dealer.

I am guessing that it may be the neutral safety switch