Ignoring memory for now...

Run performance monitor for an hour or so while the problems are occuring. Add the following counters:

Physical Disk:Avg sec/read

Physical Disk:Avg sec/write

SQL Server Buffer manager:Buffer cache hit ratio

SQL Server Buffer manager:checkpoint pages/sec

SQL Server Buffer manager:lazy writes/sec

SQL Server Latches: Latch waits\sec

SQL Server Latches: average latch wait time

SQL Server Locks: Lock waits\sec

SQL Server Locks: average lock wait time

SQL Server Access methods:Full scans\sec

What kind of average values are you seeing over the hour?