It seems that the multiple uploading function is controlled by the "STSUPLD.DLL" addon which you can find in Internet Explorer and you have the following options:
- If you remove the add-on and restart your browser, the multiple upload option is disabled.
- If you have Office 2007 installed (this is where the dll is actually located) you get the checkboxes
- If you have Office 2010 installed, you get the normal drag 'n drop
I advise against changing the upload.aspx file and/or this dll file, as you are actually trying to enable the older version. However, you perform an experiment by copying the dll from a computer with Office 2007 to the correct location ("%ProgramFiles%\Microsoft Office\Office14\") of a computer with Office 2010 installed, to see if this will have the desired result.
You can of course modify the upload.aspx file (backup the original first) and I am sure you will find many resource online, or event complete projects, but us you will soon notice, pleople actually want to do the opposite. That is, to enable drag n drop functionality when this is not available.