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St. Jude Donor '03-'04-'05-'06-'07-'08-'09-'10-'11-'12-'13-'14-'15-'16-'17
I'll chime in on the gas gauge issue. Hopefully others will help with the other issues. The gas gauge is a common problem. Try running a bottle of Techron though with your next two or three tanks of gas to clean the sending unit. Then every couple of months after that. Run good quality gas such as Chevron.
Congrats on the new Vette and good luck with the other issues.
As others have said - Techron for the fuel guage problem. I'm not sure about the vent problem you are having. Third, the shifting issue you are having is probably due to the synchros in the trans being worn. How many miles does the car have on it? It would not hurt to drain and refill your trans and rear differential with some good synthetic fluid. This made a world of diffrence for me. Also, just a word of advice, an aftermarket short throw shifter will make the shifting issues a whole lot more bearable. I have spent loads of money on my car, but the best purchase by far was an MGW shifter.
I bought my car from carmax too, and I can say the whole better quality car thing is not entirely true. They have mechanics inspect things, but if they aren't very familiar with the specific model of car, they can overlook common problems. That's what happened with mine.
They fixed one of the problems under warranty, but another they refered to a local chevy dealer that while they saw the error codes in the system, they couldn't get it to reproduce the codes while driving, so they blew me off. This later cost me $600 out of my own pocket to fix an existing issue (and a safety related one, the abs would disable itself).
Only have knowledge on the fuel issue. It's most likely been sitting a while and a fuel system cleaner/additive will help solve this problem. That and using good quality gasoline. This is mostly due to some buildup on the level sensor.
First of if there is any kind of warranty then use it. The shifting could be caused by an misaligned shifter but from what you described I think it will be your sinchros, a very expensive repair. Techron is a great way to get the gage working. Again if they warranty the vehicle make them repair it, god luck. I doubt Carmax changes fluids in their inspection so that would be first thing I would tackle after buying a used car.
with those that have said if there is a warranty USE IT with respect to the shifting issue you have.
As you may know the transmission in the C5 is in the back of the car along with the differential. A torque tube connects the engine output to the transmission input. So there definitely is linkage involved. Your issue might be corrected by a relatively simple adjustment of the shifter linkage but there may be worn or damaged parts. I would not touch the tranny myself if there is a warranty and that includes NOT touching/changing the fluid or adjusting linkage. Be on record ASAP with the dealer that there are transmission issues because they can get expensive FAST and you want the expenses at the sellers expense and NOT yours.
Hope it's as simple as a linkage adjustment..........
Disconnect the negative battery cable for 5 minutes, to reindex the heater doors. The shifter needs adjustment a common issue. Search for shifter adjustment. the C5 is a great machine congrats and good luck