Is having two different anti virus programs installed on your computer a danger to the computer? Can they conflict with each other, and should one of them be uninstalled?

The two in question are Trend Micro AntiVirus and Webroot AntiVirus with AntiSpyware.

Indeed you have solved your own question
2 A/V programs built for the same Purpose can see each other as "enemies" and If they don't "fight" they'll cancel each other out leaving you with little protection
the same is True with firewalls Have 2 on board then they block nearly everything or open a door to a "nasty" The Normal Practice is to turn off Windows Firewall and put your firewall as the main Firewall,and if that fails, or is turned off? Windows firewall steps in (as a weak Backup)

Returning to your 2 A/V Programs I'd uninstall the program that Updates the less often
I don't run either of those programs I rely on Avast! which updates daily (and is Freeware) and is very stable
For Nasties of the Ad variety I use Spywareblaster (updates roughly once per month)
and Main Firewall I have chosen COMODO which has an antivirus Program built in. This is the only configuration that is stable
NOTE This too is Freeware.Does react badly with certain other Firewalls in situ .I had a lock up when I first tried it with McAfee Personal Firewall still in place

Thanks a million Bedstor. I uninstalled Webroot. It's a long story of how I got both of them but that's what can happen when you don't know what you are doing.

I kinda figured I had screwed up after the fact, but I wanted to make sure before I uninstalled. It's my loss because I won't bother to try to get my money back because that would take forever trying to get through to them.

I tried to communicate with Webroot before I asked the question here, and was told that I was #45 in line, and I would have to hold for at least an hour.