Sue,
Thanks for posting back! I left out a crucial detail, we only have one SQL Server the previous person in my chair built (and that I am seriously considering scrapping and building new). So the "ReportServer" and "ReportServerTmp" databases are definitely gone.
I opened the SSRS Log files and here are some details that are interesting:
The <SystemName> variable is as I expected, the hostname of our single SQL Server.
Below are error / warning lines for today's freshly created log file ReportServerService__12_12_2017_03_25_14.log. It looks like there is not a URL configured at all.
WARN: Endpoint 2 is enabled but no url is registered for vdir=, pdir=C:\Program Files\Microsoft SQL Server\MSRS13.MSSQLSERVER\Reporting Services\ReportServer
ERROR: Throwing Microsoft.ReportingServices.Diagnostics.Utilities.ServerConfigurationErrorException: No DSN present in configuration file, Microsoft.ReportingServices.Diagnostics.Utilities.ServerConfigurationErrorException: The report server has encountered a configuration error. ;
ERROR: Error initializing configuration from the database: Microsoft.ReportingServices.Diagnostics.Utilities.ServerConfigurationErrorException: The report server has encountered a configuration error.
ERROR: Throwing Microsoft.ReportingServices.Diagnostics.Utilities.ServerConfigurationErrorException: No DSN present in configuration file, Microsoft.ReportingServices.Diagnostics.Utilities.ServerConfigurationErrorException: The report server has encountered a configuration error. ;
ERROR: ServiceStartThread: Exception caught while starting service. Error: Microsoft.ReportingServices.Diagnostics.Utilities.ServerConfigurationErrorException: The report server has encountered a configuration error.
ERROR: ServiceStartThread: Attempting to start service again...
If I look at the rsreportserver.config file in the <URLReservations> section, those also appear to be blank configurations, as well as the <DSN></DSN> section is blank:
<Dsn>
</Dsn>
<ConnectionType>Default</ConnectionType>
<LogonUser>
</LogonUser>
<LogonDomain>
</LogonDomain>
<LogonCred>
</LogonCred>
<InstanceId>MSRS13.MSSQLSERVER</InstanceId>
...
<URLReservations>
<Application>
<Name>ReportServerWebService</Name>
<VirtualDirectory>
</VirtualDirectory>
<URLs>
<URL>
</URL>
</URLs>
</Application>
<Application>
<Name>ReportServerWebApp</Name>
<VirtualDirectory>
</VirtualDirectory>
<URLs>
<URL>
</URL>
</URLs>
</Application>
</URLReservations>
-Mark
MSSQL 2019 Standard, Azure Hosted. Techie/Sysadmin by trade; Three years as a "DBA" now.