My 2007 Toyota Camry will randomly when cranked will immediately go dead. I can disconnect battery and reconnect and it will run fine until the next random occurrence.

Intermittent "No Start" conditions are tough to diagnose. One would start a systematic diagnosis with a DVOM of the Cranking/Charging Systems. You might have a bad Battery. Could be just a bad connection at the Battery. Could be a relay or switch. You could "Tap Test" various components in the cranking circuits. When this issue occurs...does the engine CRANK...START....then stall?

The car will crank..start.. then stall. The car will run for 1 to 2 seconds and then stall. After 3 or 4 times of repeating the this cycle the car will not crank at all almost like its not getting fuel. Then I can unhook battery cable and reconnect and the car runs just fine. The car has a new fuel pump.

When the engine does run...are there any Warning Lights ON...e.g....CEL(Check Engine Light)? With out connecting a Scan Tool to the Computer...we can only GUESS at what might be the root cause of this issue. Try cleaning the battery Cable Connections. I'm wondering if D/C the battery is erasing memories in the Computer. You might need To RESET the computer. This usually requires a scan tool capable of doing RESETS. I would be inclined to "Tap Test" the crank relay before doing another battery D/C. ALSO...does this vehicle have a Theft Deterrent System? Try this FIRST. Use your EXTRA KEY for awhile.