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Try to start out with the car ice-cold.
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Jack the rear end up, crawl underneath and inspect for rust.
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Grasp the rear wheels at the 3 and 9 o'clock position and wiggle them in
and out. If there is ANY movement and/or clunking, then normally the rear
wheel bearings AND the rear axles are shot. Figure about $300-400 a side
to fix them.
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Sometimes the bearings and axle are fine, and the problem is the two hub
carrier bushings, where the bottom of the hub carrier mates with the lower
control arm. I'll have a helper wiggle the wheel while I watch from
behind/beneath. If you can see movement where the driveshaft flange/axle
goes into the hub carrier, then the problem is obviously there. If that's
solid, and you can see the hub carrier moving around relative to the
A-arm, then the problem is trivial--a pair of new bushings and a few hours
and you're good to go.
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Lower the car onto the ground, and then go to the passenger side and jack
the right side, just ahead of the leading edge of the door, on the factory
jacking point (a circle punched into the underside of the chassis).
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Grasp the passenger side wheel at 3 and 9 o'clock and try to turn it in
and out. If there is any movement or clunking, the steering rack is
shot. However this is a simple fix, consisting of about $50 in parts for
a new bronze bushing, etc. To confirm, have a helper wiggle the wheel and
eyeball the accordion-style boot where the tie rod mates with the rack.
You will probably see up-and-down movement here, where there should be
none.
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Check the forward mounting straps for the front sway bar (where it is
mounted to the chassis). Those are known to break.
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Check the lower valance and the radiator support; these are badly designed
water traps, and tend to rust out badly.
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Rust spots on the body are at the bottom of the front fenders, just ahead
of the doors, the undersides of the doors, and the front of the driver's
side quarter panel at the bottom. Also the rocker panels and the bottom
of the door post pillars.
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Check for even panel gaps and alignment.
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Start it up, see if it starts cleanly, or blows smoke out the pipes.
If it blows smoke initially, that normally means the valve guide seals are
shot.
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With the engine running, hop inside and start actuating all the switches
to make sure all the lights, accessories, windows etc. work.
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Check for even and smooth clutch engagement.
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Once the car is warmed up, try some acceleration tests in 2nd gear,
feeling for smooth acceleration, and watching the mirror for smoke, etc.
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Wiggle the car from side to side looking for clunks etc. Also look for
self-steering under throttle, which can indicate worn-out suspension
bushings.
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Turn on the A/C and see if it operates correctly.
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When done driving, let it sit and idle for a long time - 10 minutes or
so? Check the temperature gauge and watch the engine bay for any signs of
overheating.