Hi Daylen,
Low battery is the most common reason why the light on your pen won't turn on. Replacing the batteries with new ones should resolve the problem.
Aside from the AAAA battery, there are also two size 319 coin cell batteries inside your pen. Try holding the top button down for seven seconds, and if the pen light doesn't come on, you might need to change the coin batteries as well. If the light turns on, proceed with performing the steps on this linkunder My pen won't pair with my Surface or open apps.
If the issue persists, you may have a defective pen. If your Surface is still under warranty, it's best to contact our Answer Desk and ask for a replacement.
Let us know if you have any other concerns.
Regards.