Rail services have been suspended on the Dublin-Maynooth line due to damage caused by a lightning strike to the signalling system at Clonsilla.
Iarnród Éireann said initial examination showed extensive damage that could take a considerable period of time to repair.
Intercity passengers travelling on the Dublin-Sligo route are being transferred by bus between Mullingar and Dublin.
Elsewhere, DART services in Howth are returning to normal following earlier disruption caused by an electrical fault.
The disruption comes as Met Éireann announced the level of rainfall in the capital yesterday and on Tuesday night equalled the total rainfall for August and September. Over 50 mm of rain fell at Dublin airport in this 24-hour period, compared with 14 mm for the whole of August.
Of the 400 flights due to arrive and depart at Dublin Airport yesterday, Aer Rianta said the "vast majority" were affected by delays.
The east of the country bore the brunt of yesterday's wintry conditions, with Louth, Dublin, Wicklow, Wexford and Waterford worst-affected.
Met Éireann spokesperson Mr Jerry Scully said: "The worst is probably over. . . . It will still be showery, but the showers will be scattered and it will be a lot drier."