If you've got no stats for the problematic period, you're going to have a very hard time figuring anything out.
First place I would have looked, with monitoring, would have been to see what was running against the DB that wasn't normally running, or was running with non-standard performance statistics
Gail Shaw
Microsoft Certified Master: SQL Server, MVP, M.Sc (Comp Sci)
SQL In The Wild: Discussions on DB performance with occasional diversions into recoverability