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Hard to say exactly, a great deal depends on the demand for the 8th gen Corolla and how you want to handle it (sell car outright or part out over time). Body shape, color, any cosmetic defects, trim level, what exactly let go in the engine (i.e., if there is a salvageable core), etc. all factor in to it.
In my area - a good running 2001 Corolla CE with power package and 5-speed with 100K on the clock - runs for $2500-$3500 for a private party sale. I've seen a few that were a little rough, but still ran for around $1500.
Call around different shops for an approximate cost for an engine swap. Then hit up NADA price guide or use Kelley Blue Book online to figure out what a running car in your condition is worth - subtract the cost of the repair and you'll have a pretty fair starting valuation for your car.
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2002 Corolla S, 1.8L 1ZZ-FE VVT-i
2003 Matrix XRS, 1.8L 2ZZ-GE, VVTL-i (RIP)
2009 Matrix XRS, 2.4L 2AZ-FE VVT-i
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