Filed a WV state tax form, owe income tax. I have not had a job while living here. Shouldn't pay a tax on income I don't have. Think I was misinformed, what should I do?

Generally speaking, you owe income tax on all your world-wide income to your state of residence, even if you are temporarily out of state.  This includes military deployment. West Virginia very kindly gives you an exemption for active duty military pay, but that exemption ends when you come off active duty.  However, you still can deduct your active duty pay, but you need to send a copy of your orders with your tax return and that can't be e-filed.

See this article from a competitor

https://support.taxslayer.com/hc/en-us/articles/360015908231-Is-my-military-income-taxable-to-West-Virginia-

And see this from WV

https://tax.wv.gov/Documents/TSD/tsd443.pdf

I don't understand "income you never had."  You had a W-2 from the DoD, right?  You have to pay federal income tax on that of course.  That income then flows to your WV state return.  Somewhere in the state-specific additions and subtractions there should have been a question about excluding active duty pay.  You seem to have skipped that question, so all your military pay is being taxed.

If you did not file yet, you can go back into Turbotax and fix it.  If you did file and pay, you have to wait for your return to be processed (about 4 weeks is probably enough) then prepare an amended state return to claim the exemption on your active duty pay.

I don't have a WV module installed so I can't tell you exactly where that question was that you skipped.  You can call customer support and ask them for help, they can get a state specialist to walk you through the program to find that step. 

https://support.turbotax.intuit.com/contact/