Your problem appears to be lack of memory for client connections.  How many concurrent connections do you need to support?  You may be able to fix this by changing some of your memory parameters, or you may need specialist help from MS.  If MS get your system stable, it will be worth the small amount they charge for opening a problem. 

For an 8 GB box you should normally have /3GB and /PAE in boot.ini.  Some hardware provides built-in PAE support, but it may be best to specify the flag in boot.ini.  You should also turn on AWE in SQL, and configure max memory to use about 70% to 80% of your 8 GB.  You should also look at the parameters governing connection memory, and adjust these as required.

If you are getting a very high (000s) of connections, it simply may not be able to fit in a 32-bit box, as all connection memory has to live below the 4 GB line.  As your hardware seems to be recent, it should support 64-bit - you may need to go to W2003 64-bit and SQL 2005 64-bit to get your system stable.