Well, What's a backdoor trojan? If i restarted or restored the pc

A backdoor trojan is a bad. They are a sort of virus with the capability of sending information back to the controller of it. It can be downloaded and can turn on without you knowing it and then it will follow whatever instructions it is given. The information it can send out is worse than any damage it does to your system. Passwords, bank info, credit card numbers. It can even email your contacts using your account.

System restore does record and copy these, and you need to turn system restore off during your scan and removal process. System restore does not allow virus software to remove these files.

First, update your virus program and then turn off your internet connection. Then turn off system restore by going to your control panel>System>and then click on the System restore tab, usually in the back. Close those windows and and start your virus scans. Follow the instructions after it locates the virus. If you have the option of deleting the virus, do that rather than put it in quarantine.

Since you have a program running that you don't even know about, it can certainly put a drag on your system and slow things down. Your Windows OS is so old, I can't believe it is still running. Congrats, everyone I know had a fatal crash by this time. If you need further help, please leave a comment. Thanks for your question.

A backdoor trojan is a hidden application that allows someone from the internet to take over your computer and do whatever he wants, like disseminating spam to multiple addresses, turn it into a "zombie" machine attacking other machines over the internet, spy on your habits, documents, passwords, credit card or bank details or whatever.
If you restart your computer, it will surely be there still, if it was before.
If you restore your computer (re-format your harddrive, reinstall Windows and other applications from trustworthy, original media), then it won't be there anymore most probably.

Backdoor trojans open ports on your computer, allowing attackers to execute malicious codes on your computer. Worst case senario, your Anti-virus along with other programs will not operate, and your computer could be used to attack others, an attack called Ddos (Distributed Denial-of-Service).
If a complete restoration of your computer is possible, then go for it. Else, re-format your computer and all should work out fine.

A backdoor trojan is a nasty piece of malware that let's the criminal into your computer whenever you're connected to the internet.

Restarting doesn't do a thing, and restoring only works if you're restoring from a backup that's not corrupted.

It _might_ be the reason you're running slowly, but there are hundreds of causes for Windows PCs running poorly.

Unfortunately, reinstalling Windows from scratch is sometimes the only solution. Malware writers are very good these days.

Not all "backdoor trojans" are trouble. Some legitimate software packages use them. A good anti-virus package will detect and delete it. I prefer Kaspersky and you can download it free for 30 days. If you're still running Windows 98 it will be running slow because of all the rubbish that will have built up over the years. Go into add/Remove programmes and weed out the rubbish, delete Fonts that you don't use and defragment the disk.