BRZ won't start. Cranks once.
 

So I usually let my BRZ sit for awhile and I can normally jump start it.
Last time I tried to jump it, it wouldn't start.
Swapped in a good battery and it still had the same issue.
I installed a relatively new starter and left it alone for a few weeks and tried to jump it again today, but same issue.
What's strange is that it'll crank for maybe half a second and gives up. It is a push to start.
I checked some of the relays and they look fine.
I'll be getting a fresh battery tomorrow just in case, but has anyone have experienced the same thing?

"fresh" batteries may still need a charge. Get a well charged jump pack, a battery tender or jumper cables in there

I did try to jump it with cables when the issue first started happening.
I've got a pretty beefy jumper pack that I'll try with a new battery.
Initially, when I had weak battery before, it would try to crank multiple times until the battery eventually dies out. I would use the jumper and it would be okay.
Now it just does one tiny little crank and turns off. Even with the jumper.

check your clutch switch

Check for corrosion, Are you losing power at the dash when it quits? If so it is probably a battery or connection. If not it probably is in the start circuit. A volt meter will be your friend for troubleshooting this.

Yep

Order of operations

Battery power both voltage and amps
Battery connections
Fuses/relays/switches (clutch or neutral)
If all these check out THEN starter/alternator/etc

If all these check out OK then you are into wiring and that is a nightmare

Order of operations:

Put a test light on the switch terminal of the starter. Attempt to start car. Does test lamp light up?

No that is still step 3. There an be plenty of voltage to light a test light but not start the car.
Always start at the battery and work your way out.
Never start in the middle of the circuit and work your way back.

No.

Check at the most effective test point that provides the most information at the earliest in the diagnostic.

Is it a problem on the starter motor circuit? Is a problem on the ignition switch circuit? You must know where to look before you can look, and checking everything end to end is a big dirty waste of time.

You are talking about step one of stage 3.
First make sure there is proper power and it is getting out of the source. Doesn't matter what circuit it is yet if you don't have the right amount of power. You can end up chasing ghosts if the voltage and amperage are off but your light says everything is working fine in the circuit.
If your flashlight dies is the first thing you do is grab a meter to check the switch? No, you make sure you have good batteries and they are making contact. If it still doesn't work THEN you check the switch and bulb.

It takes a hell of a lot more current to turn the starter than to light a light. And if the starter turns over momentarily then the light will surely light but the car won't start.

More current? When did I say to put the test light on the starter b+ terminal?

You are missing the point. It doesn't matter where you put a test light. It takes 12+ volts to start a car(leaving cranking amps right out of the equation) and a test light will light up with any voltage at all. Now if you were using a meter under the same circumstances then you would indeed be testing the battery AND the circuit which takes you back to my first step of "is the bloody battery any good".

I appreciate all the helpful tips so far.
I will be checking everything soon and report back.
So far, the car has a new battery that I hooked up to a tender and tried jumping as well.
Also has a new starter.
Car cranks for maybe a quarter to half a second and then quits.
Lights on the dash remain on and does not look like the power has not diminished.