If the red lights come on right away and the heat sinks are not really hot, then the heat sinks are not making proper contact with the chips. Either tighten the screws a little more or get the right height washers. you may have to remove 1 washer if you used two before. Remember it does not take long for any electronic item to overheat if the heatsink or fan are not working right. it took my xbox about a minute for the 2 red lights to start flashing if it is not done right
remove the x-clamps
clean off the old past
add new paste
replace the heatsinks with new screws but don't tighten them all the way yet
reassemble the drive but not the fans or case
plug it in and turn it on until the lights start flashing (about 10-15 minutes)
then once it is cool enough to handle tighten down the new screws
The screw should be fairly tight, but no tight enough to strip them.
Make sure that all your cables are properly re-connected. Clean out your XBox and make sure that all air entry slots are open and no obstruction is caused. also, make sure the optical drive is clean and connected right. Also, pay good attention to the two copper connectors that control the CD drive tray....good luck
BTW this is the same answer as I gave to roger on http://www.ifixit.com/Answers/View/42225/xbox360+first+flashes+3+red+lights+then+stuts+down+and+2+red#comment36645 see if it works and if not, let us know.