SSRS reachable by FQDN on local computer, but not from a different computer

Hello,

I am having trouble getting my SSRS server to successfully cohabitate with IIS, after having to move the server to a different subnet. I have 2 static IPs for that server: .242 is defined explicitly in IIS bindings, and .161 is for SSRS. I have my SSRS Web Service URL set to "All Assigned", and the Report Manager URL set to http://appreports.domain.com:80/reports & https://+:443/reports. DNS is pointing to .161. Also, SSRS points to an external database server.

What I am seeing is strange to me. I can browse to http://appreports.domain.com:80/reports on that server, and it looks great - I am at the SSRS Report Manager page, and all is well. When I call http://appreports.domain.com:80/reports from a different computer, I get an IIS error:

HTTP Error 404 - File or directory not found.
Internet Information Services (IIS)

I am not sure why IIS intercepts the call when accessed remotely. In the System log, I see this:

A Kerberos Error Message was received:
 on logon session
 Client Time:
 Server Time: 17:10:4.0000 10/29/2013 Z
 Error Code: 0x7  KDC_ERR_S_PRINCIPAL_UNKNOWN
 Extended Error: 0xc0000035 KLIN(0)
 Client Realm:
 Client Name:
 Server Realm: DOMAIN.LOCAL
 Server Name: MSSQLSvc/VM-db.domain.local:1433
 Target Name: MSSQLSvc/VM-db.domain.local:1433@Domain.LOCAL
 Error Text:
 File: 9
 Line: f09

In the ReportServerService log, there are no errors - it is the picture of health. I should also say that we are just trying to access http://appreports.domain.com:80/reports from within the local network.

I suspect there is an SPN issue, but I don't understand it well enough to comment. Thoughts most welcome! Naturally, max points on this one.