There have been people who simply changed the Civ Game to use compatibility mode for Windows XP but this is rare.
Usually, players who have the Steam Version of Civ3Complete need to add the word Unknown between PING and HOST in the Labels.text file but generally you would have already had problems long before the Third Era.
It can be helpful to open the Game and in the Civilopedia, run through all of the Units and Improvements to see if there are any Graphics Problems. Generally, the Game will report a missing file but it does not report an incorrect Graphic File such as IF a file is not a .pcx. IF this is the problem, it will show as a Faulty image in the Civilopedia. If that is the problem the image can be corrected.
Many times it is an incorrect .ini file in conjunction with an incorrect Unit file.
As Bluemofia pointed out, generally the Game does not crash but hangs if the AI tries to have an Immobile Unit Unload itself anywhere outside a city but it can cause an immediate Crash. I have seen this happen.
Check the Units that start in the Third Era at the time of the Crash. Check their .INI files and Unit files and Unit Animations in all directions with Flicster. If a Unit has a Faulty animation in only one direction, that can cause a Crash. If a Unit has a Faulty File or animation in any direction, Flicster with state that the file is incorrect and depending on the error, ask if you want to correct it...or if any direction is faulty, it will show the animation as seriously wrong visually. IF a Unit has a Faulty animation in any direction, the Unit maker would have to correct it.