Old radiators can last another half century. the pipes would need repair if they leak, but that is normal plumbing work. If you are concerned about money more than renovation, a new gas boiler is a good investment, you will gain the efficiency of the new boiler and not lose efficiency by keeping your old radiators. If you want to have new radiation because you want to to have the space the old radiators take, that is another issue that won't effect efficiency.
You can identify a steam boiler by looking at the boiler. a steam boiler will have a vertical glass tube on the side showing the amount of water in the boiler. A hot water boiler doesn't have the glass tube because the entire system is filled with water.
You can learn more about hot water heating in the 200 pages of information available free at: http://www.hydronic.net