switched to office 365 and now I keep getting prompted for a password to connect to my exchange server

This is expected behaviour.

If all mailboxes are migrated from onpremise exchange server you need to disable autodiscover on exchange server.

Try to set Set-ClientAccessServer –Identity “CASxx” –AutoDiscoverServiceInternalUri $NULL  

By running these steps/commands, you are essentially removing the on-premises information with regard to Autodiscover; thus eliminating the conflict that your end users are experiencing between the O365 autodiscover and the on-premises one.

We only use office 365 for the office app. We still connect to our Exchange 2016 server.  It's weird. It looks in at first and then it prompts for pw and never accepts the correct password while it's says connected to exchange server. The volume license version of office never had this  problem. The problem started after moving to office outlook 365. The  server will remain. They want their own exchange server. It's 2016 and fully patched and licensed.

What is the outlook version is it 

Outlook 2016 plain

OR

Office 2016 for Office 365 business - If it is this then it will connect directly to office 365 mailbox 

https://www.gothamweb.com/portal/index.php/knowledgebase/8/Outlook-bypasses-AutoDiscover-and-connects-directly-to-Office-365-mailbox.html

Office 2016 for Office 365 business - If it is this then it will connect directly to office 365 mailbox

Then you need to add registry key.

HKEY_CURRENT_USER\SOFTWARE\Policies\Microsoft\office\16.0\outlook\autodiscover DWORD: ExcludeExplicitO365Endpoint Value = 1

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Then restart your computer and it should stop trying to connect to Office 365.

Office 2016 for Office 365 business

Starting in Outlook 2016 version 16.0.6741.2017, Microsoft has enabled a new feature called Direct Connect to Office 365. If you have exchange server and this client  Office 2016 for Office 365 business is designed to connect directly to O365 then you need to add the registry key.

HKEY_CURRENT_USER\SOFTWARE\Policies\Microsoft\office\16.0\outlook\autodiscover
DWORD: ExcludeExplicitO365Endpoint
Value = 1

Then restart your computer and it should stop trying to connect to Office 365.

I can get up to this far: HKEY_CURRENT_USER\SOFTWARE\Policies\Microsoft

There is no outlook key under Microsoft.

You are looking wrong information. Look for  office and not outlook.

You need to look for outlook only after  \office\16.0\outlook\autodiscover

Please see the screenshot attached.
outlook-fix.png

Did you get the attachment?