Firstly, a Trojan Horse is not technically a virus, although it’s often considered to be one. A Trojan is actually a piece of software, that once installed, allows a malicious individual to gain access and even control of your system, when you’re connected to the internet. On the other hand, a virus is a stand alone program that performs malicious actions and propagates on its own. Trojans are named after the wooden horse the Greeks used to get inside the impregnable walls of Troy in the mythological campaign, because similarly, Trojan Horse software is installed through trickery, and usually disguised as, or with useful software. In addition to privacy concerns, Trojans can slow down your internet quite severely.
Typically, Trojans are easier to remove than viruses, but it depends on the strain. I’d recommend using a well known virus scanner, like Norton Antivirus or Trend Micro PC-Cillin. Run a scan after removing it, to make sure it’s gone.
With regard to your Internet Explorer problem, It’s possible you’re experiencing the effects of a Browser Hijack variant of Spyware. These are designed to collect information on your browsing habits, usually for marketing purposes. They’re not strictly malicious, but they are very annoying, and a privacy concern. You can remove these sorts of things with Lavasoft Ad-Aware SE Personal or Spybot Search & Destroy.
I hope that helps, without compounding your confusion
