I remove the negative bettery contact two months ago to repair
AC compressor. The vehicle sitsthere powerless for two months. Today,
I hook the bettery back and find unable to start.

The engine crank ok, then it goes woo----wooo---wooo as if the fuel
inject is pushed by someone piredically (about 1 second frequency).
When I shift to reverse, it dies 50% of time as if runs out of fuel. When I
put it to the driving gear, it die every single time.

I think it might somehow related to the fuel injection control which might
be affected due to the power cut off. Any suggestion before I send
it to the shop?

Thank!

Bad fuel? If fuel sits for more than a month it becomes less volitile. It will not ignite as easily. Also water in fuel will also cause the simptoms described. You can buy an additive from a parts store to remove water from fuel and restore volitility.
Also expect it to run horrible for about ten miles after reconnecting battery for PCM to relearn.