I'm getting exactly the same error message; I'm running Windows 7 Professional 32-bit.
I was able to start Apache but the module status in the control panel was yellow not green. I checked if anything else was running on port 80 using netstat -o but nothing was. So I stopped Apache, and then tried to start it again and got that same error saying "session cache is not configured".
I opened httpd.conf and changed the port for Apache from 80 to 8045, and restarted Apache. This time it worked, but again when I bounced it it wouldn't start up again.
I really needed XAMPP on my laptop for a meeting tomorrow, so I've just gone back to XAMPP 1.8.0 which installed perfectly and ran straight away on port 80.
It seems to me that there is definitely a problem with Apache on XAMPP 1.8.1. I'll be happy to help tomorrow night once I've got through the meeting and I can reinstall XAMPP 1.8.1 if you need any more details.