We have just performed this operation on two PCs, a dead desktop and a dead laptop.
It was a long haul though, and most of the suggestion over at How to convert laptop drive (with a dead laptop) for use as VMware image? were of limited use.
What didn't work
We tried creating a new VM with both raw disk access and it's own virtual disk, cloning one to the other (using clonezilla) and then running the VMware convert utility on it, but that resulted in VMs which blue screened on boot, so that wasn't a solution.
We tried the create a new VM, attach the raw hard drive to the VM and convert method, but that just gave a cryptic error message with the current
We tried looking at the solutions on ServerFault for Convert a hard-drive into a VMware machine but most of those solutions had too little detail to get us past the problems we had with those suggested solutions.
The solution that we settled on was suggested by Dave M in that his answer though.
We downloaded and installed the trialware version of Symantec System Recovery Server Edition (which is currently Symantec™ System Recovery 2011 Server Edition FREE 60-day Evaluation!).
We then created a one-off backup of each target hard drive (one for the desktop PC hard drive we had, one for the laptop hard drive), creating two recovery points. Then we performed a one-off conversion each to a virtual machine.
We selected the option to Run Windows Mini-Setup and Split virtual disk into 2 GB (.vmdk) files. The former substantially reduces the time to get the resulting VM up and running, while the second allows you to transport VMs around on memory sticks that don't support >2GB files/
We then booted each VM in VMware Player, the Windows mini setup ran through quickly, installing the new virtual drivers & replacing the old real drivers.
Finally we installed VMware tools on each VM and let the VMs pick up the new VMware tools optimised drivers.
The only downside with this method is that it does require re-activation of windows, so make sure you have noted down the product key of the dead machine before you start.
Note that we tried this procedure on a Windows 8 PC first, but couldn't get SSRSE to run after it was installed, so reverted to using a Windows XP machine (on the same hardware). We assume that when the trial gets upgraded from 2011 to 2013, this problem will go away.
Before this I've only ever virtualised running machines and the process has been quick and painless with VMware converter. I was amazed to find out that virtualising a dead system from it's hard drive alone would be so much more involved, I just assumed that VMware converter would just have an option to do it.