I don't ever remember giving my Irish bank my PPS number, are you sure Cashier?
But since they got so serious about money laundering it was much more difficult to open a new account even with my own bank. They're very strick on ID (Passport of ID card will do for that) and proof of address. For this I was able to use utility bills but Redshoes won't have that.
Redshoes where do you plan on living when first you arrive? Maybe it would be a good idea to use a relatives address and from there apply for the PPS number from Social welfare as a starting point. Then down to the driving licence section to get an Irish driving licence etc.