'You may not have any other clients (that is computers or devices dependant on the router) but if you have, is the password you mentioned (more anon) the one you enter when you connect that device to the internet..
I know nothing (relatively) about eircom and the routers they supply, if you got it from the ISP, but some routers use a system called WiFi Protected set up. That relies on a facility in both router and client that is not (as far as I know) in the iPod Touch. It is a sort of press button to set a password scheme. One reason I don't use it is that you don't see what it has done.
Usually router encryption passwords are not shown in clear for obvious reasons so you cannot read it. Sometimes the password can be read in the keychain.However you say your password is 'as quoted' .
Next thing is I hope it is not as stated. You should not quote a password in the forum. If it is your password are you sure it is the wireless encryption password and not the router's administration password. The form 'eircom12345678' looks like a default router admin password. You should change from the default as soon as you set up the router but aside from that the router admin password will not link a client, the iPod, to the router.
These issues to do with wether this is the proper WiFi password aside you may have entered the password wrongly. I use a 62 character WPA passphrase (a piece of poetry in fact) and new to the touch screen I had to enter it from an Apple Bluetooth keyboard to be sure I made no mistakes. Your password as quoted is easier.
If you want more information on the various passwords to do with routers, how to get round a forgotten router password, how to (possibly) trace a password in keychain, post again.