1 long beep then 3 short beeps is the motherboards troubleshooting beep code, make sure when you researched it you were on the correct motherboard manufacturers website, or else you could looking at a completely different issue. (Different manufacturer = different beep code meanings) Look in your motherboard manual or on your motherboard manufacturer's website and you should be able to narrow it down further to a specific piece of hardware.
Seeing as it seems like an overheating issue, use a program such as
Speedfan (free) to check the temperatures. If your unsure of what's safe for your hardware, post back the temperatures and the hardware in your computer and one of us will tell us whether it's in the safe range.
It could also be an issue with the seating of the videocard or memory modules. Try opening the case and reseating these parts. Try booting with just one memory module, if it still doesn't work, try using just the other memory module. While your there it's a good idea to clean out as much dust as possible, just don't use a vacuum cleaner. (really, don't, it can remove transistors from your parts) You can use a cloth to lightly wipe dust off the parts, just be very very careful with raw circuitry such as the motherboard. Make sure all your fans are working and aren't clogged with dust. If you have a portable fan (like a desk fan or something) try taking off the side panel of your computer and blow the fan directly onto the hardware. This should lower your temperatures significantly and determine if that's the problem.
I'm not sure how much you know about hardware, but make sure when taking off the side panel you take off the right one, or else your motherboard and everything attached to it will fall to the ground. (Obviously not good

) The correct one is the one on the left when you're facing the front of the case.