2005 Malibu Classic 4 cylinder won't start

i would run or put a test light or small buzzer at the fuel pump wire close as you can to the pump and just start giggling the wires / relay/bulk head connectors/grounds.. and listen to the buzzer for a change in pitch...really...you gave some good info BUT was the power after the relay also 7 volts and zero at the same time... you need to rule out when and where 12 volts stops...could even be the ign.switch...

Agree with Kelly,but all so check your ignition switch,there was a recall on this,and if it was done it may be bad again.

There is a constant 12 VDC at the relay as long as the ignition is on. Yes it was recalled but the "fix" during the recall had nothing to do with the ignition switch itself. GM's answer was simply to "fill in the hole in the ignition key". The original key had an oval slot. If the key had excessive weight e.g. a heavy key ring, then the weight of that might cause the bottom of the key to turn counter clockwise and shut off the ignition. By filling in the hole then any weight the ignition key would support would be centered in the middle portion of the key minimizing the twisting affect on the key and ignition switch. I don't know. Seems like a band aid. GM designed the switch to be easy to turn and therefore turn off again. But the price to fix it right is higher than the price of customer safety or loyalty.

one side of your relay is going to have 12 volts that is the load side the other side should have 12 volts for 2 seconds a prime. when testing a fuel pump relay use a test light not a volt meter i would have a long explanation on the meter way to long. at the pump if you turn your key will it light a test light for 2 seconds if you crank you car should be 12 volts at the pump for more than 2 seconds. i would check your grounds and wires at the pump and install the new pump