Hello jillian,
Welcome to Microsoft Community.
I fully understand your anxiety about not being able to use your computer at this time.
From your description of the problem, I noticed that you mentioned a key point, the LED light of the power adapter does not seem to be on:
The LED light is not on, which means that the power adapter is not powered up, so the Surface Laptop Stuido will shut down when the battery is exhausted.
I believe that you've read some of the information in the following support links, because you seem to have made some efforts, such as cleaning ports and replacing different outlets:
What to do if your Surface power supply or charger doesn’t work - Microsoft Support
Considering that you have exam needs in the near future, I recommend that you try another way to charge your Surface Laptop Stuido, namely with the USB-C port.
The Surface laptop Stuido has two USB-C ports:
For devices with USB-C port, you can try charging temporarily with USb-C in the case that the power adapter cannot be charged:
USB-C and Fast Charging for Surface - Microsoft Support
Please read the information in the link above, as there are some requirements for the specifications of the USB-C charger, and low wattage chargers may not be able to charge the Surface device*.*
However, if there is no way to charge it at this point, my final recommendation is still to contact the Surface technical support team and send the device along with the power adapter to them for inspection or repair:
How to get service or repair for Surface - Microsoft Support
You may need to find another computer for warranty order creation. Also, let me kindly remind you here that sending the device to the Surface support team for repair may take about half a month, so this may affect your exam. Instead of sending the device directly to after-sales support, perhaps I should recommend that you buy a new power adapter:
Buy Microsoft Surface 127W Power Supply – Microsoft Surface
Because get a new power adapter usually takes much less time than repairing the device.
Best Regards,
Mitchell | Microsoft Community Support Specialist