First thing I'd check is whether your download folder has write permissions. Such as trying to install mIRC in a way where it tries to keep the download files below c:\program files\.
Were you seeing an error message in the "status window" when receiving a file? By default, mIRC installs mirc.exe into the folder where you install it, but uses c:\users\username\appdata\roaming\mirc\ for placing mirc.ini and puts the download folder as a subfolder beneath that. Pasting these commands into any editbox shows what is being used as these folders:
//echo -a mirc.exe is located here: $mircexe
//echo -a mirc.ini is located here: $mircdir
//echo -a downloads go here: $getdir(test.txt)
Note that download location can differ if you have defined a different location for different filetypes, so you might need to use test.zip or test.jpg instead.
Another problem could be your firewall settings. The first time you try to download a file using each c:\pathname\mirc.exe it asks if you want to allow it to download files. If you click NO, it won't ask you again, so you'd need to either install again elsewhere or edit your firewall settings.
You're vague about why you can't connect. Is it only that network you can't reach, or are you unable to connect to all networks? If you've installed mirc so it tries to use a read-only folder, that can also affect how mIRC tries to connect, as it would have trouble writing settings to disk for the next time it tries to run.