Can you boot into safe mode ?http://www.pchell.com/support/safemode.shtml
avast doesn't run in safe mode and so presumably the same for Norton, so there shouldn't be any possible conflict.
This is where it becomes complicated - Chicken and egg from here you could uninstall avast first or Norton using add remove programs. I don't think you should uninstall both as you need at least one working AV if you are to go on-line to a) view the information about using the Norton removal too on-line or b) downloading the off-line removal tool.
1. I would say uninstall avast first from safe mode and reboot and see if that at least gets you back to square one. If so continue, if not report, though I'm not entirely sure what to suggest if that happens.
2. I assume you saved a copy of the setupeng.exe, the avast installation file on your HDD, if not get that and disconnect from the internet. So you are ready to install it after the next step.
3. Now uninstall Norton using add remove programs and reboot.
4. Install avast and reboot.
Report how you got on, don't try the Norton removal tool just yet.