I filed my taxes w/turbotax. both were "accepted. Irs website says "processing" 3.5 mo. later. transcript they sent says "no return filed." do I refile? what's going on?

No, you do not file another tax return.  The transcript is not available because the IRS has not completed the processing of the tax return.

After the tax return has been Accepted by the IRS (meaning only that they received the return) it will be in the Processing mode until the tax refund has been Approved and then an Issue Date will be available on the IRS website.
See this IRS website for federal tax refund FAQ's - https://www.irs.gov/refunds/tax-season-refund-frequently-asked-questions
If over 21 days since being Accepted by the IRS and the tax refund is still Processing you can call the IRS and speak with an IRS agent concerning your tax refund.
Call the IRS: 1-800-829-1040 hours 7 AM - 7 PM local time Monday-Friday
When calling the IRS do NOT choose the first option re: "Refund", or it will send you to an automated phone line.
So after first choosing your language, then do NOT choose Option 1 (refund info). Choose option 2 for "personal income tax" instead.
Then press 1 for "form, tax history, or payment".
Then press 3 "for all other questions."
Then press 2 "for all other questions."
- When it asks you to enter your SSN or EIN to access your account information, don't enter anything.
- After it asks twice, you will get another menu.

Press 2 for personal or individual tax questions.
Then press 4 for all other inquiries
It should then transfer you to an agent.