[KimMG]

Check your battery cables making sure the connections are clean and secure (both ends). Make sure all the connections at the starter are clean and secure. Check you belt make sure it is not slipping. Test the output of your alternator (new doesn't necessarily mean good). Make sure all the alternator connections are good.
Dan Masters drew some good wiring diagrams and they are available at advanceautowire.com. Make an enlarged copy for yourself, it will help in tracing problems.
The following two sites have good technical articles:
mgbexperience.com
britishcarforum.com