Desktop only load in Safe mode

Hello,
I have a Dimension Es21-Dell. I am a dummy when it come to computers so bare with me. When I turn on my computer, it get to password and then the screen is black. I found out from my kids that there were 2 TROJAN viruses and they had been quaritine. I dont know if this is the cause of my computer not working. I have my operating system and drivers & utilities disk. I tried to backup my files in safemode but no such luck. I shouldve been doing that before the problem, I will soon as I can fix it. I need to know where do I go to install os and du? Can I copy my files and put on external drive? Where can I go in safemode or whatever mode to back up my files? I dont have my ISP startup disk. Can I copy that and put on external drive or dvd rw? Please help me. I have kids that want to take over my laptop because they cant run virus scan everyday on their desktop.