Determining cause of system slowdowns

Hello all, hoping you can help.  We have a RedHat box that two days ago
starting having periods of slow performance.  The slow down is bad enough
that you can see it when trying to type at a terminal and some processes,
such as SNMP, don't respond.  Users have also been disconnected.

The last change that was made was applying the normal monthly patches on
2/7 (the problem only started showing up yesterday).  According to the
information from 'top', the system seems to be fine.  A typical snapshot
looks like this:

Tasks: 282 total,   8 running, 274 sleeping,   0 stopped,   0 zombie
Cpu(s):  1.1%us,  0.3%sy,  0.0%ni, 98.5%id,  0.0%wa,  0.0%hi,  0.0%si,
 0.0%st
Mem:   3909268k total,  1669580k used,  2239688k free,   231832k buffers
Swap:  6094840k total,        0k used,  6094840k free,   972756k cached

Any ideas on where to look?

Thanks!

Mike