I filed my tax return a week ago. My state return status still shows pending on Turbo Tax, but when I check the return site for Virginia it has no record that I’ve filed

MY RETURN IS IN PENDING—what does that mean?

Did you e-file?  Did you click that big orange button that said “Transmit my returns now?”  If so, your return is now in “pending” on a server.  Do not try to change anything while your return is in pending. If your return is rejected you will be able to make corrections before re-filing.

The IRS just began accepting/rejecting 2020 returns on Friday, February 12, 2021.  You need to watch your emails for the acceptance/rejection notice that may take until mid-February or later to arrive.   And watch your spam folder too.   There are a LOT of e-files on servers so it may be several days after the IRS opens before you get an email.  There are so many returns waiting —kind of like trying to put the ocean through a garden hose.  

When you e-file your federal return you will receive two emails from TurboTax.  The first one will say that your return was submitted.  The second email will tell you if your federal return was accepted or rejected.  If you e-filed a state return, there will be a third email to tell you if the state accepted or rejected your state return.

A state return cannot be accepted until the federal return has been accepted.  And it is very common for it to take an extra day or more for the state return to be accepted.

https://www.irs.gov/newsroom/2021-tax-filing-season-begins-feb-12-irs-outlines-steps-to-speed-refunds-during-pandemic