The laptop would be using the same internet connection as the now dead PC, so your IP would be the same. You would be at risk of losing your nations.
If it is only temporary until you get a new computer to access (from a network apart from your wife) then i suggest you request a nation sitting permit. That way your nations can legitimately share an IP temporarily until you can get it sorted. Do not share networks unless you get that nation sitting approved though. It will also mean you two can never interact again.