Well YES, replace the wire. Don't you ever look under the hood? Also it sounds like you need to get a new 6 year battery of the right size and install a new regulator on the alternator. You may not need a new alternator. You don't say how many miles are on your car. Alternators usually give up at about 130K miles (250kms)
Anziani
'97 CL500 156K
'97 CL600 47K