I ran into this situation after I had jump started my car with reversed jumper cables and blew the fuse on my OVP (Over Voltage Protection dohickey). My battery was really dead from sitting around during repairs. My car accelerated very slowly with the OVP fuse blown. After repair, and with a really hurting battery my car still did the same thing. With help from the forum I was told that a crappy batter won't cut the mustard. With new, fresh battery, problem went away.
During the problem though My dash lights, ABS, ASR, etc, would flash.