Brought my 2002 XK8 Coupe out of storage few days ago...hooked up battery started up...then came the noise...main belt and a thumping noise...a very short time later...smoothed out...after sitting for a few days...started and same thing happened...I know I have to have this checked...but, any thoughts prior to me bringing it in? Thanks in advance!!!

 

With the squealing it is most likely a worn belt. Attached is a picture of the tensioner showing the wear indicators. The thumping could be the belt or a worn idler or tensioner puley. I have attached a picture of the belt arrangement.
I would replace the belt and check that the pulleys turn smoothly. If they feel gravelly or don't rotate smoothly replace them also. The idler is available at most auto parts stores. The dealer will tell you the tension pulley has to be replaced as an assembly. The updated ones do but the original tensioners use the same pulley as the idler so just buy 2 idlers if needed.

 

Don't discount the possibility of contamination. Double check for greasy deposits and check for possible sources, like a leaking water pump. Typically, belts develop cracks as a sign of wear. Squealing is more contamination. If you unsure of the history, as these belts are not expensive, just change it. Follow Vern's advice and rotate all accessories/pulleys/tensioners by hand for any sign of wear.

Good luck, keep us posted.