I can't get my MAC OS X Ver. 10.1.2 PowerPC G4 on the internet through an ethernet cable.

Could the following article possibly be of interest to you?

Connecting to the Internet via cable, DSL, or local area network (LAN) in Mac OS X v10.5 or earlier - Apple Support

Unless otherwise specified, DHCP is a frequently used method.

If you need additional information, please post back with the type of Internet connection (cable TV, DSL, fibre/LAN, etc) and the name of the Internet service provider. Also, please indicate the make and model for any connected devices (such as modem and router).