How can I start my Corvette without having to go to the dealership to get a new key? My money situation is tight, so I'm trying to find a way to start my car, without having to pop the clutch or order a new key.
Short answer, you can not.
Your car is equipped with an immobilizer. With out a properly coded key/transponder chip you will not be able to start your car. It disables fuel and spark. Its possible you could get the immobilizer tuned out of your ecu but this is much more complicated and expensive so not worth mentioning plus you would still need a key to unlock the steering.
Your cheapest method will be to get a key from dealer with your registration and photo ID, then program the transponder yourself. Your easiest option is to call a mobile reputable locksmith to come out and generate a new key and program it for you.
Terrible answer - find your lost key
If you know its definitely destroyed or overboard at sea then you're out of luck, but if you just misplaced it then look very hard everywhere it could be.
Can you can afford to wait a couple days and see if it turns up? Think back, retrace your steps, check the pockets of any item of clothing you were wearing since last time the car was driven.
Check coat/jacket pockets, check under furniture. Ask anyone who lives in your house. Get a flashlight/torch and check in the car. Check under the car. Can you get into the boot/trunk still? Check there.
Check your laundry space, your mailbox, inside your vacuum cleaner.
Look all through your dog/cat's bedding, and your own bedding. Ask your kids. Check your fridge/freezer (yeah really) and behind your toilet bowl. Check inside any cupboard, and the floor of every wardrobe space.
Ask your neighbours if they've found any keys. Dig through your rubbish/recycling bins (before they get emptied!)
If you find your key, then you'll save a ridiculous amount of money. Get a spare key at that point - its often that you can open the door/boot with a key but not start the car.
I had a flatmate who lost his only car key. A locksmith came on site and probed out a new one. A couple days later I found his keys, which had fallen out the window and were in the garden outside. Would have saved him $hundreds for the callout.