Yes, a loose belt will cause many problems, the alternator not charging anf the water pump not cooling the engine, power steering not working, A/C not working, and you are not the first person to have put the belt on wrong. Many mechanics who are not familar with LR's do it.
Before youbuy anything else make sure that you get the belt on right first.
I know it can be very frustrating when you are not 100% sure of what you are doing.
Let us know how it turns out.