continuous long beeps is RAM...
try as following remove both sticks and clean em (the copper area) with a white rubber (ya, a rubber for pencils writing...) and boot the pc only with 1 stick, if that doesnt work turn it off again and try with the another one... and u'll get ur deficient ram. if that doesnt solve ur problem, most likely ur ram socket is wasted up. anything could happen if u got low tension or something, even if ur comp if shut down. best way to avoid that kind of problems is buying a psu or something like that, or even turning off the PS when u turn off ur comp (when u turn off ur comp ur PS stays at stand by, doesnt completely turn off, thats why some motherboards have some Led light, letting u know that PS still is powering ur motherboard.
try that i mentioned, u said that u changed ur mobo, well then it MUST be ur RAM. maybe both rams r fkud up... wish u the best luck ^^