have you checked the fuses? Are you sure the battery is good/charged?
Ok, those are the easy ones to check, and easily overlooked. Always start with the simple stuff. If the old alternator was not charging the battery, and you haven't checked/changed the battery - it's more than likely dead... hence the non-working high amperage stuff (lights aren't that high amp draw).
Things like the fuel pump, turn signal flasher units, and starter relay/solenoid are all sort-of high current devices.
The only thing that doesn't make any sense to me is the hazard lights working - it's on exactly the same circuit as the turn signals... there are 2 flasher units - one for the turn signals, one for the hazards. Maybe one is a heavy duty unit and needs just a bit more current to switch?
Outside of that... Hooking up an alternator wrong will only kill the new alternator (fries the diode pack inside it nearly instantly)... I think you have a dead battery, but the other things not working may be symptoms of:
corroded connectors in the wiring
bad/loose/corroded ground connections
corroded tabs/connectors on the relays (there are only a few) - possibly bad relays.
blown fuse(s)
bad hazard switch (they corrode internally and if you switch it back and forth several times, it may clear up the turn signals... you can also carefully take the switch apart - noting exactly how the parts go back together, and clean it).
Bad fuel pump.
Bad fuel.
several other possibilities, but start at the top of the list (the battery) and go from there. /ubbthreads/images/graemlins/thumbsup.gif
Got a picture of your car you can show us?