have you tried running MemTest86?
http://www.memtest86.com
From the POST (power-on self-test) beep codes you mentioned, it definitely seems some sort of RAM failure. Check your motherboard specs to make sure the memory is compatible with your motherboard.
You may want to update the BIOS, take caution if you are not too sure how to do it and make sure to backup your data just in case. If it does not work, then try the new stick by itself to be sure it's working, remove your old memory and put only the new memory into the same slot as the old one closest to the CPU.
Some memory issues can be simply solved by inserting or aligning it properly, make sure the part you are inserting lines up with the raised plastic notch inside the memory slot. Memory can only really be installed in one way, so if you got it to click down and both sides latched it was probably in correctly, but best to check it all out to be sure.
If you know the slot itself works that means no issues with the motherboard, it's either partially faulty memory, or memory incompatible with your motherboard. I would want to say look into the voltages and DRAM settings in your BIOS but would highly urge you not to mess around with these if you are not sure what you're doing.