Chris,

If the seller didn't provide you with any of the documentation that should have come with the bike, I would suggest you re-contact the seller and ask some specific questions. If it's a LIFEPO4 battery, was it original or a post-purchase upgrade. If an upgrade, who was the vendor and what version of BMS does the battery have, most importantly, what's the amperage rating for maximum continuous discharge. You also need to know specs on the controller if the seller still has any. Is this a conversion kit bike or a bike bought outright as an e-bike. If you can give some info, maybe people can help point you to some online documentation.

If you have a friend who has a volt meter, you might ask to borrow it. Otherwise, they're fairly inexpensive and can be found at most hardware stores. Using one will be able to pinpoint problem that may reflect a short or other electrical issue impeding proper functioning of electrical components. If any of your friends have motorcycles, maybe they could help you test the throttle and controller.

If this bike truly has a LIFEPO4 battery, I'm more inclined to think there may be a problem with the discharge ratings--not enough for the controller--and that the BMS is shutting the battery down to protect it when you hit the throttle. If you get the bike moving through pedaling and then slowly depress the throttle does the battery still shut down?

Good luck, you should be able to pinpoint the problem.