the HIGH and LOW screws on the deraiulure ONLY change where the shifting STOPS, they are limiting screws, if it wasnt shifting into the highest or the lowest gears then you would adjust these, or if it ws OVER shifting and the chain was falling between the frame and rim, or cluster and hub, but for everyday maintenance, its best to leave them how they are.
The problem more than likely existst in the cable tension, which can be fixed by putting the bike in the Highest gear possible(this SHOULD mean there is no tension on the gear cable for the rear derauilure) Using a 4mm? allen key undo the cable at the derauilure, and wind adjustment nuts ALL the way in, pull the cable tight and do up cable retaining nut. go thru the gears with the bike on a stand, and idjust the barrels as required.
IF you NEED to touch the H and L settings, SMALL adjustments make a BIG difference.
This site may also help...
Park Tool Website
or if reading is to much.. Watch a Video!
How To Adjust Your Rear Derailleur - Bicycle Tutor
oh and make sure you post in the Pushie Picture Thread
As for replacing the chain, it should only need to be done when the chain rings or the cluster is changed. dont skimp on the new chain either, get smething decent, better to pay an extra $5. and get a good quality chain that will last and mesh correctly with the gears than a cheap one that will snap or stretch in a short amount of time causing you more headaches.