Ok I know this sounds stupid but is the new battery full of acid and charged? and is it connected the correct way round.

Have you measured the battery voltage and some basic volt chassing?

If you have tried fuses, try starter relays.
At the side of the battery there is a cluster of relays, ignore the yellow one as this is the turn signal relay, there should be two smaller black ones try changing them/checking the connection or take them out and give them a light tap on a solid surface on several of the sides.

You can thank me later

sounds like the new battery aint been charged
daft but worth a check

Lily, if the optimate is connected, what do the lights say?

If the lights dont come on the battery is faulty.

If they come on except the top one (green) its charging, fully charged when the green light illuminates, this may take a couple of days if the battery is very low.

Have you checked to see if the battery is full of acid?