The issue here is the semantics of Equal. In the cancelled case, the expression fileName == $Canceled is comparing a symbol with a symbol (the same symbol) and so it can resolve to True. In the other case, it's comparing a symbol with a string, and that is indeterminate (according to the designed semantics of Equal anyway). So that If cannot be resolved because the condition cannot be resolved to either True or False.

There are several possible fixes. One is to use the 4-argument form of If:

If[
 fileName == $Canceled,
 fileName = "Canceled",
 fileName = "File has been found",
 fileName = "File has been found"]

In this form, the last argument is the one that gets executed if the condition doesn't resolve to either True or False.

Another fix is to use SameQ rather than Equal.

If[
 fileName === $Canceled,
 fileName = "Canceled",
 fileName = "File has been found"]

SameQ checks for structural identity, and so it always resolves to True/False.

You could also use Switch or Which instead of If.

I must have lost the plot somewhere along the line ... I have this

fileName = SystemDialogInput["FileOpen",pFilename, WindowTitle -> StringJoin["Select the ",pFileDescrip," containing dissociation constants"]];
         If[fileName == $Canceled,fileName = "Canceled", fileName = "File has been found"];

When the dialog shows, if I click on "Cancel" or close the dialog without selecting a file, fileName is returned as "Canceled", as it should, BUT if I select a file and click on "Open" fileName is returned as the name and path of the file instead of "File has been found"/

Thank you - I can see that being very useful

It (my confusion) was the former - how to combine multiple statements together. It just looks a bit alien when you are used to the if then .... else ... end if construct as in, for example, Visual Basic

Yes, you can use If for this.

If[
 True,
 Print["true 1"];
 Print["true 2"];
 Print["true 3"];,
 Print["false 1"];
 Print["false 2"];]

...should do the three "true" prints.

If[
 False,
 Print["true 1"];
 Print["true 2"];
 Print["true 3"];,
 Print["false 1"];
 Print["false 2"];]

...should do 2 "false" prints.

If you don't want the false branch at all you can do...

If[
 condition,
 TrueStuff[],
 Null]

The Null can be implicit:

If[
 condition,
 TrueStuff[],]

And though it's undocumented, you can leave out the non-true branch(es) entirely:

If[
 condition,
 TrueStuff[]]