The ports may be blocked on the ADSL or in your router/firewall. Whether you can web or telnet into your ADSL and do some tweaking, only your provider can tell you.
I imagine the ppl telling you to connect on port 59 are using dcc server. (view/options/dcc/server). You have to enable it and then dcc requests need to be made to the ip, not the nick. In any mIRC window, type: /help dcc server for more info
Re identd, port 113 may be blocked, and/or they are blocking identd requests. It may be necessary to run a standalone identd server if they wont open it. Altho this is a DALnet url, the info is pretty good and may help you:
http://kline.dal.net/exploits/ident.htm also click on "windows identd" for links to standalone identd servers if you find you need one.
As a side note, just a reminder to please be careful about accepting files as many contain trojans or illegal content.
