If you have no spare key, a full set change is often cheaper than new keys from Fiat. Fiat should be able to supply keys from your VIN number, and the dealer will code them to your car. But car would need to be take to the dealer.
If changing a full set of ECUs and keys, you need to ensure it is from a same spec, or higher spec than yours. e.g. aircon, electric windows, mirrors, locking, foglamps, etc. Any items on the donor vehicle but not on yours can be disabled using
MultiECUscan software, but bits can't be added as far as I know.
You'll need, engine ECU, body ECU, keys and locks, as a set. Try to get a set with both keys!
Once changed of course, you'll lose the option of a new key from Fiat using the VIN, unless you have the VIN of the donor. Small worry if it fixes the problem.