Only the IRS will know what all they are doing with your return, but we can tell you some things you need to check.
What do you mean by "my refund was accepted March 4." Did you mistype? Do you mean your efiled return was accepted to begin processing on March 4? Or is that an approval date at the IRS?
The IRS says 9 out of 10 filers who efile and choose direct deposit will get their Federal refunds within 21 days after being accepted. Some returns are processed fairly quickly, while others require additional processing due to specific items in the return. Some are pulled at random for more thorough investigation.
If you efiled, double-check to be sure the return was efiled successfully and accepted. If you used Online TurboTax, you can sign into your Online Account and check the efile status at the Tax Home.
If that showed it was accepted, you can use the "Where's My Refund" tool at the IRS website below to monitor the status of your Federal refund.
NOTE: When using that tool, be sure to enter the SSN and filing status correctly. For the refund amount, use only the Federal refund amount, and not any total refund amount that includes a state refund.
The amount to use is on your Federal Form 1040, Line 21a.
To track a state refund:
Have you checked Where’s My Refund? it has the most up to date information available about your refund. The tool is updated daily (usually overnight) so you will just usually need to check once a day.
It takes about 21 days to receive your refund from the IRS when you e-file and choose direct deposit as your refund choice. Also you will get personalized refund information if you check back with Where's My Refund? once the IRS has processed and approved your refund.
For more on the timing of your refund please see this TurboTax FAQ.
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