Checkout the <a href=”http://live.sysinternals.com/”>Sysinternals toolkit</a>. Particularly the <a href=”http://live.sysinternals.com/procexp.exe”>Process Explorer</a> application. This will help you track down what is using up server resources. Download the entire <a href=”http://technet.microsoft.com/en-us/sysinternals/0e18b180-9b7a-4c49-8120-c47c5a693683.aspx”>Sysinternals suite</a>. These are Microsoft utilities now so no worries about malware.
The <b>first thing </b>that I would do is to perform a malware scan on the server. If the server is clean, then I would verify that the system clock is set correctly (particularly the AM / PM setting). Exchange performs several maintenance tasks on a nightly basis, and many of these processes are very resource intensive. If the slowdown happens at 3:00 pm, but the clock indicates 3:00 AM, then the maintenence cycle may be running in the middle of the day.
You also mentioned that the server only has 1 GB of RAM. That is only enough memory to support a few mailboxes. I would recommend using Performance Monitor to see if your server is running low on RAM or if it is running short of Page Table Entries (PTEs). If so, then you will want to add memory to the server, and you may possible want to remove the /3gb switch from the boot.ini file if it exists.