Hello and welcome to the forum.
Cluster issues are quite common on the 500, though this is one of the more unusual manifestations.
If this happened immediately after changing the battery, that needs further investigation before rushing to replace the cluster; most faults are the result of the last thing that happened to the car. It's possible, though unlikely, that the new battery could be defective; you'll notice spurious electrical problems long before it refuses to start. Even batteries which test OK have been known to cause such issues; indeed it's sometimes said that the best way to test a battery is to put it into a S/S 500 and see if everything works as it should.
Changing a battery could disturb the earth connection (another weak point), so it's worth checking that carefully, particularly the point where the earth lead connects to the chassis.
I'm also wondering what else might have happened shortly before the battery was changed (for example, jump starting the car, or fast charging with the battery in situ, or connecting anything directly to the battery terminals - a 'no-no' on S/S equipped 500's). It's possible a spurious voltage spike could have fried the electronics inside the cluster.
If you do need a new display, you have three options:
1. A
new cluster (not cheap; a franchised dealer fix won't leave you with much change out of £1000; parts, coding software and cables probably about £600 if you do it all yourself)
2. A secondhand cluster from a breaker. You need to buy one with less miles on it than your car has covered; they can be adjusted up, but not down
3. Sending your existing cluster for repair; probably midway in price between the two other alternatives.
With options 1 & 2, you'll also need Fiat-specific software such as
MES to code the replacement cluster to the car. Option 3
may be plug 'n' play.
@
typecastboy probably knows more about cluster issues than anyone else here - he 's fixed quite a few, and is both knowledgeable and helpful.