Just yesterday I installed a new water heater (WH) --- tuned off the cold supply at the water heater, turned off the main supply at the house (as back-up) drained the water tank, disconnected the water supply lines and the LP gas line. Removed the old water heater. Installed the new WH, connected the water supply lines, connected the gas line. Turned on the water supply at main house valve and cold supply line -- filled tank. Lite the pilot, turn the LP on to setting of "2"... within 30 minutes I had hot water!. The problem is the water pressure in the lower half of the house is 1/2 less water pressure then upstairs. What could have caused that?

Any time you shut off the water, sediment, lime, pieces of copper (that is already stuck in the line) settles. Turning the water back on will send that obstructive material throughout the pipes.

Take an aerator off a sink in the lower half of the house. You'll see what I'm talking about.

XenoSapien

Is both the hot and cold water affected the same or is it just one of them that is lower than the upstairs.

It effects both hot and cold

It really sounds like knocking some crud loose is the problem. If cleaning the aerators doesn't fix the problem, you will have to work back further. You will need to remove the faucet cartridges and clean or replace them. Note, hot water heaters need to have either the inlet or outlet open at all times. Unless you have an expansion tank, you must open a hot water tap as soon as you close the inlet.