Dysonmedic dot com has excellent articles and pictures.
In the DC04 section the switch clearly has four connections - Live & Neutral both switched - a Double-Pole switch.
If your replacement switch has only two connections then it's a single pole switch and unsuitable - you have the wrong switch.
Are you absolutely sure the switch is defective? Has its operation been properly checked/tested?
A common fault in vacuums is a broken wire inside the cable near the plug - cut off about 6" and fit a new plug - often works wonders.
Good luck...
Peccavi
February 2013