I just recently got a '68 camaro from my in-laws. I put a brand new battery in it, new oil, primed the engine. They said it was running before but then sat for 15+ years. It has a 350 in it. I tried starting it but got this annoying buzzing sound coming from near the horn. When i tried to turn it over it wouldn't click some of the lights on the outside work but none of the dash lights work. I'm guessing from sitting so long. I also have hardly any experience with cars besides fluid changes and brake/tire work. Anyone have any ideas on what could be the cause?

 

It's probably a good thing it didn't start if it's been sitting that long, without some preparation you could have caused a lot of damage if it is a salvageable engine and that's questionable after that many years.
Has it been stored indoors? Heated storage? Dry and warm or wet and cold climate area? At the very least you should pull the spark plugs and get some oil in the cylinders and let it soak in for a couple of days, a dry start with rusted /stuck rings will destroy your engine pretty fast.
After getting it oiled up I would spin the motor over with the plugs still out a few times using the starter, it will turn over easier with no compression and you'll move the oil around on the cylinders and maybe loosen up the rings.
The carb will most assuredly need a rebuild especially if there was gas left in it when it was last shut down. It might start but probably will run poorly and likely die soon with a gummed up old carb. I'd at a minimum pull it off and soak it in a can of carb cleaner overnight fully submerged and then blow it out with compressed air. It's still probably going to need a rebuild or traded in as a core on a rebuilt carb but maybe it will run a while. Is it a stock engine with a stock intake and carb? As for getting it to turn over you probably need to clean or replace the battery cables, even with a fresh battery if there is corrosion you won't get enough power to the starter. Both ends need to be clean and in good condition, sounds like your ground is bad at the very least. Pretty good chance the rubber parts of the fuel lines will need to be replaced and any filters inline or at/in the carb, hope you drained out any old gas and put in fresh gas at least. There will be a lot of things before you can drive it safely like rebuilding the brake system and replacing the lines. Another thing I'd do before trying to start it is pull the valve covers and spin the motor over to make sure all the lifters are moving the pushrods and rockers, a stuck lifter can destroy your cam if it starts up that way but you can pull the intake manifold and unstick a lifter or replace one that's stuck. Does the car still have the stock points fired distributer? If so I'd get a points and condenser set for it or again at least clean it up with some WD40. Do your homework before you do damage to your very cool new ride by not prepping it to come back to life. Auto trans or manual? 10 or 12 bolt rear? Posi? Tell us more about what you have and how it was stored.

 

Good suggestions given and with plugs out, either squirt in oil into cylinders and/or WD40. A soaking is needed, then crank over with plugs out.
Externally charge battery.
The buzzing you hear may be the Key Buzzer due to ign key in ign switch with drvr door open.

 

OP welcome to the forum, as it has already been said you have a lot of work to do on the car before its safe to even start much less drive. Cars don't like to sit for a long time, sitting for this long will require some work to bring it back to life. The plan to pull the plugs and spray some oil or WD40 in the cylinders will help lube the cylinders, may even want to try turning it over by hand to see if the motor is frozen. The ing system may need some attention, what is the car running? If it still has the old points system I would swap it out for a pertronix ignition setup just to get it running. Had one in my 65 Chevelle wagon and it worked great. Drain all the old gas out and put some fresh fuel in, replace the fuel filter, like it was said the carb will likely need work but it may let you try to start the car. Watch out for fuel leaks, the old rubber hoses may be dry rotted. What tranny and rear are in the car? What type of brakes does the car have? Is there a power booster or is it a manual pressure system? Also your started solenoid may be frozen in place if it did not even try to tick when starting. The cooling system will need to be flushed and the hoses replaced. Also watch out for the rubber lines going to the heater core, they will likely need to be replaced.