I recommend 1st gen Tundras to anyone that asks. Mine is at 170,000 trouble free miles. Well, except fot the 4 O2 sensors I've changed, and the usual tires, gas and oil maintenance stuff.
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I use the Mothers Back to Black on my trim and tonneau cover, they both turn grey over time. The paint gets a good buffing about twice a year (or more as needed) most times simply running over it with a cleaner/wax using my cheapie orbital buffer shines the paint up to showroom (if you ignore the deeper scratches)
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The 5-speed: I'd love to swap one in place of my 4-speed. Not that the 4-speed is bad (mines gone 170,000 afterall), but I think 1st gear is a little lower and that would be cool in the woods.
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If the truck has a tow package it should have a transmission cooler. Double check for it. If it does not have one swap in the biggest aftermarket cooler you can fit. Mine is a Long Tru-Cool.
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The 04 was indeed a non-VVTi and a 4-speed combo with 4.10 gears
The 05-06 went VVTi and 5-speed. I think they went back to 3.91s but some may be 4.10s.
I'm halfway sure all DCs were limited slip rearends, if you look there should be a tag on the diff cover with the letters LSD.
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I wouldn't hesitate to buy a 2000-2006 Tundra AC or DC, if the price was right (and I needed a truck)
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Oh yeah since its a beach truck be sure to crawl underneath it with a flashlight and look for rust. If you see any in the floors or the frame tap it with a screwdriver and make sure it's still solid.....not usually a problem, but with salt water exposure it never hurts to be sure....