My car won't start, maybe something with the battery or electrical.

I have a 2002 Nissan Altima in which it
won't start. When it does start it won't allow
me to go over around 5 mph. It won't
accelerate over that speed limit. Once you
have driven the car for a little the battery
dies right away. We have had to recharge
the battery several times but it still won't go
over the amount of around 5 mph. I have
recently replaced the starter and had a new
engine put in about 5 months ago. I highly
doubt it has to do with those two things. We
might think it needs a new battery, but
would a battery only allow you to go 5 mph?
Maybe it's the electrical? Thanks