Hi Alex,
HTTP management isn't a feature I'm used to, but might the following help...
"show ip http server all" - Gives a small history of http sessions.
That in conjunction with a "show flash" and checking the last modified date/time of the startup config might help you.
You might get lucky with "show log history"
There may well be a better way, but that's all I can think of!.
HTH
Kevin
Might it be possible that the switch was restarted without a copy run start and the startup config had all the ports shutdown?