it didn't even dawn on me that it might be a search box. Dohhh..!
Don' sweat it...

. From your screenshots I see that on the theme you are using the page name
'search results' is missing (the page after you click on HDA). In the standard theme it is present and that gave me a clue, because, well, I hadn't realize it was a searchbox either
Now when I enter, say *.* in the search box, I can see a list of all the files I remember saving on the server. However, I can't open them, or download them either.
That could be browser related. If I click on a file different things happen according to the browser I use:
Opera(10.62) tries to open:file://localhost/C:///hda/Music/Amy%20MacDonald/Amy%20MacDonald%20(2007)%20-%20This%20Is%20the%20Life%20~/Amy%20MacDonald%20-%20This%20Is%20the%20Life%20-%2001%20-%20Mr.%20Rock%20&%20Roll.flac . Nothing happens. The '%20' (ASCII 'space') are probably fine, but the "file://localhost/C:///" part isn't.
Firefox (3.6.6) tries to open:file://///hda/Music/Amy%20MacDonald/Amy%20MacDonald%20(2007)%20-%20This%20Is%20the%20Life%20~/Amy%20MacDonald%20-%20This%20Is%20the%20Life%20-%2001%20-%20Mr.%20Rock%20&%20Roll.flac. Again nothing happens. "file://///hda" probably isn't correct.
The only browser I tried, that worked, is ironically,
Microsoft IE8:
file://hda/Music/Amy%20MacDonald/Amy%20MacDonald%20(2007)%20-%20This%20Is%20the%20Life%20~/Amy%20MacDonald%20-%20This%20Is%20the%20Life%20-%2001%20-%20Mr.%20Rock%20&%20Roll.flac. Now it asks me to open or save the file and both actions work correct.
Sorry for the hard to read lines, but they are cut & paste examples from an actual file.
But as Bigfoot65 said before, there would be no need to use the browser. you wrote:
I tried this, assuming that (in my remote computer running Win XP) you're referring to the Start > Run, then enter \\hda in the open box. This entry wasn't recognized, and an error message was the result.
Are you sure you typed '\\hda' and NOT '//hda'? When switching between Linux and Windows this can be confusing. I use HDAConnect3 on remote computers running XP and Vista and it works fine for me.
Else I'd suggest to first try to access your hda this way with a local (windows) client before using HDAconnect3, as this adds a layer of complexity.
Richard