Hi Jim. I'm Greg, an installation specialist, 9 year Windows MVP and Independent Advisor, here to help you.
If you access your mail by a browser (which you can always do anyway), then try another browser. Then try resetting the browser.
If this is the WIndows 10 Mail app what works most is to go to Mail Settings (gear icon at bottom of Inbox) then Manage Accounts, then choose the problem account(s), then Delete the Account.
Restart PC and retrace that path to add the account back. Make sure the Sync settings are as desired for how far back you want mail Downloaded from, whether to include Calendar and Contacts (People app).
If that's not enough then Reset the Mail app at Settings > Apps and Features > Mail & Calendar > Advanced Options > Reset. Restart PC.
Finally if nothing else works reinstall the Mail and Calendar app from Option Two here: http://www.tenforums.com/tutorials/3175-apps-re...
If you have broader performance problems go over this checklist to make sure the install is set up correctly, optimized for best performance, and any needed repairs get done: http://answers.microsoft.com/en-us/windows/wiki...
Start with Step 4 to turn off Startup freeloaders which can conflict and cause issues, then Step 7 to check for infection the most thorough way, then step 10 to check for damaged System Files. Then continue with the other steps to go over your install most thoroughly.
If nothing else helps then run a Repair Install by installing the Media Creation Tool and choosing from it to Upgrade Now. This solves many problems and will also bring it up to the latest version which you need anyway and by the most stable method. http://windows.microsoft.com/en-us/windows-10/m...
I hope this helps. Feel free to ask back any questions and let us know how it goes. I will keep working with you until it's resolved.
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