Car just died, electrical system gone

well the battery is now dead (or only discharged !)
cause #1 ALT/Gen replaces WRONG, see here 10,000 times. more www.

driving a car the ALTERNATOR produces all Electrical power.
100amps x 13v is 1300watts, and runs ALL>
when it dies the battery is sucked dry/dead/ discharged.

1; remove neg lug from battery or BOOM (100amp fuse BLOWN)
2; remove ALT
3: new one back connected same.
4: battery NEG lug back
bingo no BOOM.!
every SM manual of every car tells that;.

you said didn't want to start
but I guess you meant starter is dead, or clicks only or will not spin fast as it must.

the 15mins is dead accurate, for 50 years driving seen this happen
as ALT goes dead at night,
in the day engine runs 30min to 1hour dead ALT , HEADS off

the blow fuse is just bay fuse
or worse, a fuseable link, oddity not fun to fix. ever.
thus step 1,

no engine told but let me look on uSA car thjis.
2010 not AVEO5

there it is but what it looks like, hummmmmm

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)

Did you check the main fuse under the seat near the battery?

It looks like you have a short somewhere. You would need to inspect all the wiring related to that in order to pin point the problem. Also check if there is another system working from that same fuse. ie. Power Outlets. Sometimes if they go bad it will blow the fuses shutting down everything else.
I hope this helps!

u have a dead short on main live wire check for overheated wires

Or the battery cables ! Do you know how to use a voltmeter ?
Starter Voltage Drop
Do you know how to do basic automotive electrical testing ?
How to voltage drop test starter motor circuit
Electric Testing Techniques You Need to Know Here is a place to view wiring diagrams ! http://www.bbbind.com/free_tsb.html

Double check the battery positive connection wiring carefully as it commonly has connection problems when the battery is changed.

Has the stereo been changed recently? If not move to the cigerett lighter. These two are most likely the prob. But you could have a bare wire anywhere grounding out. Good luck and hope you find it.

Check power connection by fuse panels under hood just below the center of windshield

When a fuse blows something is grounding out in the system you need to find where it is grounding out and replace the wires that are bad, as well as whatever the bad wires messed up. eg.. guages. etc.. I hope this helps you out.