I am a little confused about what you are trying to explain and hope I am getting it right.
When you installed a new battery, the problem immediately occurs means power is not getting to the starter or insufficient power is getting there. When dash lights are dim, it means either the battery is weak or connections are loose somewhere.
Jump a cable from the negative terminal of the battery to any part of the engine and test if there are any difference. If it resolves problem, check the ground cable from battery to the transmission/engine. It could be broken or connection is bad.
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Monday, January 15th, 2018 AT 8:16 PM