Is the voltage constant while the motor slows down? How, when and where did you measure the 1.5V?
It is over 9V when measured, but below 12V, which is why I said around 10V.
Sorry, that is really vague. What do you mean?
Please qualify all measurements with an explanation of the conditions. Example
"I measured 1.5V across the motor terminals while the battery voltage was confirmed to be 11.5V and the motor is connected to the shield, set to 100% output in software"...
The supply voltage stays constant. The voltmeter I have shows its range - between 1.5 - 9V, 9-12V, 12-17V and >17V. the motors don't show any voltage, and the supply is consistently in the 9-12V range. Regardless of when the motor is spinning, the meter doesn't show any voltage. The IC's are burning hot though.
Doesn't that tell you something? 
Why are you running a 1.5V motor on 10V, anyway?
While the supply measures between 9-12 V and the output is set to full speed in the code, the motor terminals show less than 1.5 V when connected to the shield.
Also to note, the arduino is being supplied by 5V through the USB as stated in the original post, the motors are being run through the external power.
I will state the obvious. A 1.5V motor should be powered with 1.5V. It's probably drawing too much current and forcing the drivers into current limiting protection mode.
We have tried everything from 3 volts with the USB all the way to this point with no luck. The higher voltage, the more it is starting on its own, and when I looked through the other forums most of the time the answer was that the voltage wasn't high enough.
Yes, but I am currently getting less than 1.5 V in output after putting 10Vs in, even though the only thing connected is the motor. If this is the case, is the output really going to increase if the input is lowered? I will follow your advice though and try it out. Give me one minute.
Your approach is based on guesswork and experimentation. That's okay when things work. When they don't work, you need to use engineering. The device data sheets are available online. Those will explain the features, caveats, and limitations.
Which is why I am here 
I am new to all this, doing it for a school capstone project. I watched a video explaining those, but I didn't realize that each company had a separate one, which is why I didn't realize that I overloaded it with the double a batteries earlier.
The "this" that you are new to, requires that you at least begin to adjust yourself to a methodological, knowledge based approach. The very purpose of a Capstone project is to build those kind of skills.
I watched a video
Mistake. Go to the original documentation. That stuff is 89 times watered down and recycled.
I realize that, and I did watch multiple tutorials doing similar projects, figuring out what parts I needed, how to code the arduino, learning the app that goes along with this and such. I am learning, I just need a little guidance with this, and am trying to reach out and taking your advice as you reply. This is a high school project, and most of the teachers I've asked have no clue, which is why I'm here.
Once again,
did watch multiple tutorials
STOP watching and READ. There is far more information on that board and it's applications online, than you will ever see in a thread like this. GOOGLE.
Post #26 I gave you a pretty likely cause for the behaviour, you just need to go investigate why it is happening.
Learn how to make current measurements, not just voltage, and check those all around to see if they are sane.
Get as much documentation as you can find on all your devices and begin comparing specs to see if they are compatible.
Thank you for that, I am working on following that advice.
I don't currently have an ammeter, otherwise I would have provided that, and as for getting compatibility, this set has worked in other cases, so they should work - this is just a motor shield connected to an uno and dc motors - so far, it should work because these are what are meant to be connected. I took out the module.
Spend the $10 if you can for a DMM. It includes an ammeter, usually.
Now, the motor doesn't run at all, even after turning it.
is there a different shield you know of that would work better to your knowledge?
You may have burned up the rotor windings by applying an overvoltage. Check continuity with an ohmmeter.
I don't know. I think the better motor drive modules are not shields. I have some of those...
Yes, but nonetheless, those parts have to have compatible specifications and connections to work properly.
The bare fact that something worked once, means something but not a lot in this business. It's about meeting, and slightly exceeding, properly tested limits (that is usually done by the manufacturer).
How many motors?