you apparently have a loose connection somewhere. reseat the memory, electrical connections etc. make sure while plugging in any molex connector that they are seated firmly. Once in a while, a single wire may pop loose from the connector housing and go unnoticed leaving you with the predicament you're in.
Tap the edge of the motherboard with a screwdriver handle while powering up the puter to see if there is any change in inconsistent start up. Hopefully that will lead you in the right direction. Report back your findings.