before you go buying parts just like that trying analyzing things first because if you never done it before you could waste alot of money...
usually when a iphone is on and charging it vibrates or if you turn the silent on and off... the phone vibrates. regardless, if this happens, its a display issue and the lcd could be disconnected or defective...
now if you plug the iphone into a computer or ihome device and nothing happens within 15-30 mins, that could mean a number of things... logic board short circuited, power, or dock connector... or a software problem...
you could take out the logic board and plug up the battery to it alone along with the dock connector and plug into a computer... this would allow you to see if its a power issue... if the computer reads the iphone, power issue is not the problem.. and the dock connector is ruled out...
at that time, detach everything and reattach the lcd first then attach the battery then dock connector to the logic board and plug in a cable to the dock connector to see if it comes on... if the lcd does not turn on but still read by the computer the lcd needs to be replaced...
if nothing happens AT ALL after replacing the dock connector, battery and lcd, which is the problem i am having with my iphone right now, then the logic board might need to be cleaned or we have a goner...
there are ways to check for software issues... what i usually do is download this program called tinyumbrella... when you have an iphone stuck in recovery, you can use this program to kick it out of recovery mode. this program can also read an iphone that is stuck in recovery mode when itunes cannot, so definitely a plus...
if you plug the iphone into the computer and tinyumbrella or itunes cannot pick it up, something is wrong hardware-wise because tinyumbrella is able to pick up an iphone in the worst of worst software situations...
these are just my suggestions... i welcome anyone to correct me if im wrong...