You can enable debug logging as per here -- How to enable Xtrace Diagnostic Logging -- (check in the comments for a simple "copy & paste" .reg key to enable it all). You can do that inside the WINPE image as well.
That may give you more data to begin with.
Also - check any LDDWNLD / other logs (go by "latest datetime stamp") and check what IIS has to say on the Core. If IIS doesn't have a log entry for that file to be even poked, youc ould have DNS issues (try using the IP).
Play around with PEDOWNLOADER (can be done in WINPE and Windows environments) to duplicate / test things (such as IP vs NETBIOS name vs FQDN). Details can be found here -- How to use PEDownloader.exe to Duplicate / Troubleshoot Software Distribution .
Start with that & go from there ... once you have an error message that's helpful (preferred server, etc) that may put you on the right track more naturally?