After battery replacement in 2003 xk8, all electrical came on, but no start. No crank or anything.

 

With ignition on, what gearbox position is illuminated on the centre console?

 

I am assuming the battery was installed and immediately no crank. If that is correct, start with a multi meter and check voltage on the posts and then check the voltage on the outside of the clamps. If there is a difference then the posts are dirty and need cleaning. If the voltage is 11.5 volts or less even though a new battery the starter relay will not engage. It isn't unusual for the voltage to be low on a new battery from sitting on the shelf.
If the battery is reading 12.8 or more volts then it might be the starter relay.
Under the hood on the passenger side at the back of the engine bay is a box with relays. The starter relay is in a group of three and is the one closest to the front of the car. The other 2 relays should be the same color. Pull and swap with one of them. If it then starts the relay is bad.
Give it a try and get back with results and if needed we can continue searching for an answer.

 

Also check that the battery cable connections are good. There have been some reports of cable ends that need to be crimped more and it may not be evident until the cables are removed and replaced.

 

I had a problem with the ground strap crimp and replaced it with a solid old-style ground cable. Cheap fix (at least it was for me).