When replacing battery wires starter engages. Sould this be the solenoid sticking? Would an one recomend where to buy another and how hard to change?

 

Remove the main 12 volt fuse, and make sure the two big heavy gauge wires on the solenoid (one to the starter and one to the battery) aren't shorted together somehow outside the solenoid. If it still cranks the starter when hooked up then your solenoid is bad.

The solenoid is just a remote controlled switch. Applying 12 volts across the two small low current wires drives a coil that magnetically pulls a bar across the big stud terminals shorting them together and connecting up the starter motor through big heavy gauge wires. By removing the main fuse above it eliminates any possibility of a wiring error or short applying 12 bolts across the small wires erroneously.

Solenoids are easy to change. It's only four wires and a screw or two. Ebay sells them. What kind of quad are we talking about?

 

It's a bit more unlikely, but it could also be that the ignition button on the handlebars has broken somehow. You'd probably feel a difference when pushing it but I'd still check it with a multimeter.

If you don't already have one, you can get a cheap multimeter for less than $10 at Radioshack. It'll be invaluable to solving any electrical problem you might have with your ATV. To check wiring and switches, just put it on the ohm (or resistance or horseshoe-like symbol) and, with the battery disconnected, put the meter's two leads on an exposed part of the switch's two wires. A reading of "0" indicates the switch is closed or "on". If the solenoid or switch read closed without you touching anything it means it probably needs to be replaced.