I downloaded this desktop image from openclipart.org and wanted to delete the blur (halo) (or is it a gradient?) around the PC and screen. But I can't seem to find it in Inkscape. I already ungrouped it all and looked about in XML editor, but no sign of it (at least not recognisible by me)?
Can anyone give me a hand and tell me where or how to find the blurred objects?

Select the object and ungroup it (Ctrl+Shift+G),
then deselect the object on top (Shift+click)
and delete the blurred object (Del).

OK, thanks Lazur!
But why is it that clicking on the blurry borders doesn't select anything?

After your explanation, I found the blurred object by ungrouping, then deleting one by one the objects top to bottom until the blurred one was deleted. Then Ctrl-Z and I could select the object in question. It's a strange one (to me at least). When it is selected and the node tool is activated, no nodes appear. Properties are as follows:
id=g5759.
style: fill:#000000;filter:url(#filter5827)
transform: matrix(0.90406,0,0,0.90406,-25.855,-2.1125)
no other properties.

Filter5827 has properties:
id: feGaussianBlur5829
inkscape:collect: always
stdDeviation: 1.3860982

What kind of object is this, how is it created? It's a filter, right? But it doesn't seem to have a source object?

By the id it is a group with a simple blur filter.
You can select filtered objects by clicking only in the area of the unfiltered object.
And, because it is no larger than those covering it, you cannot click to select it
-unless you use Alt+click after entering the group (g5831) of the desktop and shadow.

Ok, got it! Thanks!!