You don't recover from the capture of your capital province, and you may not even see the details of the battle that finished you. If another great power's capital province is captured, all of that nation's ships sink, but its army units continue to defend their provinces until all provinces are captured. (A minor nation, on the other hand, can continue to function in its usual way after its capital has gone, even to the extent of buying goods after every one of its provinces has been captured.)
Every great power's capital is a seaport or a river port, which can be blockaded by enemies. The game does not make clear whether a minor nation can be blockaded, but it is clear from battle reports that your merchant ships trading with them may be attacked in unexpected places not adjacent to your capital's "anchorage" sea zone.
Every nation's capital starts life with a level 1 fort.
All of the controllable industry in your nation is deemed to happen in the capital, whither freight cars (in Imperialism) or roads or ships (in Imperialism 2) carry things such as resources and materials for consumption or processing or sale.