Indeed, 10.6.3 and Intel Core i3, 5 and 7 processors are not supported, in fact Apple shot themselves in the foot, as Mini Mac's and iMac's with Core i processors needed an updated version of 10.6.3 to work pending the arrival of 10.6.4. So as stated stay with a pre 10.6.3 DVD or wait until Apple release a 10.6.4 DVD.
I just tried to install SL using the new 10.6.3 DVD and yes, you the dreaded "A virtual CPU has entered the shutdown state..." from VMware. This isn't a question of patching to 10.6.4 before rebooting, it won't even install.
You need the 10.6 Retail DVD (10a432) to install on VMware. If you have 10.6, install that and do a Software Update and all works fine. But you cannot currently install from the 10.6.3 Retail DVD. These are my results on a Core i7 processor on a ThinkPad T510.
I had SL running fine on my Core i7 laptop, until I upgraded to 10.6.3 then "A virtual CPU has entered the shutdown state..." I re-installed and stayed at 10.6.2 until 10.6.4 came out and all works fine, fortunately I had a 10.6.0 DVD to do the re-install.
Indeed, VMware cannot compensate for restrictions within the guestOS, and 10.6.3 does not support Intel Core i3, 5 or 7 and from your experience Xeon 5600 processors either. I can only suggest using a non vanilla kernel, or trying to get hold of an early OS X DVD, i.e. 10.6.0. Sometimes life sucks!
This is the Vmware Build I have installed with the unlocker
I have the retail dvd, i ordered it from apple store they sent the 10.6.3. royally sucks if its tied to that specific version. Its probably my processor, even though they are supported from vwmare.