Blown head gasket?
 

I recently purchased a 94 and noticed the radiator was running hot at idle. Coolant is brown with sludge in it. Had a buddy look at it and he thinks it's a blown head gasket. Am I totally screwed? How much do repairs on something like that usually run? Could I fix it myself?

Remove each plug and examine each one closely.

Before you remove the plugs, Check each ignition cable.
Is each cable firmly attached to each plug?
Are any cables damaged.

Number each plug with Tape went you take them out.
You will not remember which one went where.

If all 8 plugs have nice tan color, your good.
If some are caked with sludge or oil, then you may have a problem.
Keep notes on which plugs are good and which are bad.
If you find a Bad plug, go back and match the number to the Ignition cable. Is that cable bad?

Buy or Borrow a compression tester for the cylinders.
Surf YouTube for other people compression Results for your year corvette.
Run a compression test on each plug. Take Notes.

Send pictures of the Good Plugs and the Bad plugs [if any].

If you are planning on keeping the car long-term, then after you solve original issue, Replace ALL fluids and start from scratch.

Good luck
Miles

Welcome to the forum, Reed. A compression test and a radiator pressure test will also help diagnose this problem. A complete coolant system flush would probably be a good step in the restoration process.

When pressure testing radiator don't forget to test the cap too.