93 3.8L Engine pause problem

A little while ago my car started having this problem where i floor down the accelerator and there is a quick pause, but during that pause my lights dim in and out and there is a slight click sound, this started to happen around when i got a new battery, but i brought it back to the battery place and they said the battery was fine. Ive heard that it could be the fuel pump...but i dunno...any suggestions?
Thanks.