The way it works is that every time the magnet goes past the pickup it uperates a switch in the pickup, this is wored to the computer holder and the computer counts the switch operations.
1. Ensure the pickup and the magnet are VERY close together, then waggle the bike back and forth so the pickup is going past the magnet. Look for life in the computer. This usually fixes it.
2. If no joy, then remove the comp from the holder and get a short length of wire, a paper clip etc. Use this to short across the little metal pips, then remove the wire and put it back on a few times for say 15 secs. If the computer is working it will register a speed.
3. If your comp will not count the switch operations, it's dead. If it does then you may have a broken wire to the holder (very common, sadly) and you need an electrical test meter (
Maplin, £5) to test this.
If it's where the wire goes into the holder then the way to prevent this in future is to take an electrical tie and tie the wire very firmly to the handlebars so that the wire doesn't waggle about, get caught etc.
These are your 3 commonest failures. I've had each of them and buy the same model of computer for all my bikes so I can interchange parts when they break, but I'm geeky like that.