I used the Web Installer. Worked beautifully. Operated portal for several weeks and did minor fiddling. Then it broke with an error message I didn't understand. I thought, "Well, since I'm not that far into it, instead of troubleshooting, why don't I just reinstall?"

I deleted the folder and ran the Web Installer again, but now the wizard says:
Connection Error(s):
Index #: 0
Source: .Net SqlClient Data Provider
Class: 20
Number: -1
Message:

I can't connect to the database with the SQL Management Studio either.

What's the next step? Uninstall SQL Server and delete the folder and start again?

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"All the solutions are simple, but only after you already know them" Robt. Pirsig

Restarting the machine and re-invoking the Install Wizard, now produces 3 error messages:

Connection Error(s):
Index #: 0
Source: .Net SqlClient Data Provider
Class: 11
Number: 4064
Message:

Index #: 1
Source: .Net SqlClient Data Provider
Class: 14
Number: 18456
Message: Sql login failed

Index #: 2
Source: .Net SqlClient Data Provider
Class: 0
Number: 5111
Message:

Where should I look to see what needs to be changed?

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"All the solutions are simple, but only after you already know them" Robt. Pirsig

So, I removed IIS, I removed SQL Server Express, I removed the Web Platform Installer. I deleted  the database in AppData and the wwwroot folder, and then, went back to the Web Platform installer. No errors during the installation. Installation Wizard begins, gets to the Configure Database Connection page, and again gives a connection error:

Connection Error(s):
Index #: 0
Source: .Net SqlClient Data Provider
Class: 20
Number: -1
Message:

How come?

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"All the solutions are simple, but only after you already know them" Robt. Pirsig