Yes, you are pretty safe if you don't switch on the machine.
Why might you become infected, there could be several reasons?
Basically your security, both programs and user behavior, has fallen down and allowed an infection to pass through your defenses.
How many users are on your computer besides you? Do you know their surfing habits? Are your users using an Administrative account rather than, the less damaging in case of problems caused by malware, Limited User account?
With Administrative privileges anything which gets into your machine can do whatever it likes, but if you are only a Limited User then any damage is limited too.
Programs like virus scanners only mainly concentrate on viruses (and some more common worms and Trojans), but that still leaves many worms and Trojans as a danger. Which is why many people have what is loosely termed a "layered approach", where you have specific programs for specific threat attacks. You can spend lots of money preventing the chances of infection but the biggest danger is from sloppy user control.
Another thing to watch out for (besides E-mail) are portable media such as DVD's, CD's, SD Cards, or USB, shared and inserted by friends from other less controlled machines.
No matter how good your virus scanner is, unless it knows about an infection threat (updated definitions) it will not detect it, although many have heuristic detection to advice of a possible infection or suspicious file, which produces as many false positives as it does positives.
To help your virus scanner manufacturer/programmer you could send them a copy of the infected file, via a zipped file and E-mail so that they may better handle it in the future.