Depends which bulb is the "second" one. There's no standardization on the testers. One bright light and one dim light probably means either the neutral or the ground (we can't tell from the description) is not connected.

If all the connections are tight on the receptacle you replaced, you'll have to check earlier ones in the circuit.

Trust me the connections are tight. I didn't put in back in the wall after testing it for the fifth time. The problem is all the other outlets and light switch in the room work just fine. I did do voltage check with a multimeter(?) this morning and while the other outlets read 120.7 volts. The outlet in question is 00.3.

What about the connections on the "other end" of the cable that's supplying your outlet? Are the connections tight there as well? There's a broken connection somewhere. Might be time to call an electrician.

I'm not sure where the line leads. Its the only outlet with one hot and neutral wire. All the other outlet in the room have two each.

It sounds like an illegal installation, if you haven't a clue what you're working with, it is time to call an electrician. The presence of enough induced load to light the light dimly most likely points to a piece of wire connected tot he receptacle that is not connected on the other end to *ANYTHING*.

I'm not sure where the line leads.

It's time to make an educated guess. Choose either the outlet to the left or right of the problem outlet and open it up and check the connections there.

Thanks Greg 2010, your right. Its not like I don't have the time. Can't afford an electrician and I enjoy trying to figure things out.

It could also be an outlet on the other side of the wall in another room. Basically, odds are that it'll be the closest outlet.

While you are opening up the outlets, I'd suggest moving any 'backstabbed' connections to the screws. The backstab feature is notorious for causing bad connections.

And wrap the wire clockwise around the screws so that it gets pulled into the screw as you tighten it.

Greg2010,
Thank you so very much for your help. After two trips to Home Depot (who knew they made outlets without the green ground screw)the outlet is working. I ended up having to replace the other three outlets in the room. One of the outlets was badly corroded on the neutral side. There was one with the wires in the back like you mention so I undid that one. The last one was slightly melted on the neutral side. After I finished, the outlet that originally wasn't working, worked just fine. As it turned out there was nothing wrong with it. So thank you again.

mori1,

What you are describing does not sound good.

Is the wiring in the walls that you are working with copper or aluminum?

Does the wiring have a "grounding conductor" aka a "ground" running along with with the hot & neutral?