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I won't give you any advice as I don't own one yet, but I had considered going the route you're considering, but have since decided against it...I'm going to wait until I have enough money saved up to buy a nice one...you never really know what you're getting when you buy a beat up one...
You can find out what is triggering the check engine light. Bill Curlee and 8VETTE7 have posted the how to thousands of times. Search "pulling codes".
If the check engine light is for something simple, you may want to continue checking out the car. Don't be in a rush to buy because it is a CORVETTE. You want a Corvette, you don't NEED a Corvette. Be patient. You will know when the right one comes along. I looked at 30+ cars before I found THE ONE.
I have been searching for the right one for about 18 months. But my patience was rewarded 6 days ago. I was able to find a 2000 6-speed magnetic red convertible with every option but mag wheels and Z51 package. All for $10,800. The deals ARE out there!
Be patient and you'll find the right one.
On the other hand for $6,000 you could romp that thing around for a summer and unloaded it next spring, all for the price of a late 90's camry. :
once again would encourage one to wait
that 6500 car will probably cost thousands to get up to snuff and you still have a hi mi car worth about..6500.
Many guys keep the miles low wait for one of those to pop up. Cars that are neglected usually need a whole lot more than what you initally see it will be endless and youll never want another.