Can you use an rcl 3000 lamp with a dead battery by plugging it into the wall?

No. The instruction manual for the RCL 3000 "Rechargable Remote Control Lantern" specifically states that the 120V House Current Adapter will not power the lantern and is only for charging the battery.

You can replace the battery though...

Brand = SkyTech

Model = SC 46

Volts = 6 DC

Ah = 4 (or 4.5)

ApexBattery.com has them as of 1/30/2011 @ $7.95 each.

Note: There are other tricks you can do to make the lantern work without a battery, but it requires knowing a little about electronics.