MoMoune: I've finally found out what is exactly messing with the game speed (well at least on my rig).

It seems that the real problem is the game having trouble to deal with the default system recording devices. By chance all my motherboard recording devices were unplugged and that's why switching to my motherboard audio ship fixed the game speed.

I took a screenshot to be as clear as possible.
All you need to do is to disable your main recording device in sound panel while the game's running (Alt+TAB), and it should be fine. One of your recording device is messing with the game max speed which is messing with gods animations, etc...

I'm using win7x64 so I have no idea how to do this using winXP but it should remain possible to get the same result with a bit of searching.

Detailed solution for win7x64 (or see screenshot):
1) be sure that any program that uses any audio feature is closed otherwise it won’t work (Steam, Web browser, Movie/MP3 Player etc,...) Reboot if you’re not sure.
2) right click on your taskbar speakers icon --> "Recording devices".
3) enable everything if you don't know or your main recording device if you're sure.
4) start the game already.
5) ALT+Tab and right click on the main recording device --> "Disable".
6) Get back to the game, game speed should be fine now (and so gods apparition and combat should be much better) Try the last tutorial to see Apollo against Cyclops combat. If the game speed is fixed Apollo should kill him after ~1month (at 100% speed) otherwise, could be worse than one year...
7) if it doesn't seem right, ALT+Tab again and try enabling/disabling each recording device, no matter if they weren't all enabled before, game needs to see the right one go from enabled to disabled while running.
*) Starting the game with all recording devices disabled won't work sadly, it needs to be disabled manually after each time you've started the game (except if you have a default working integrated audio ship). Not so bad, sometimes you'll prefer to simply keep the turbo mode (fast city growing) then quiclky alt-tab if it ever becomes game breaking (gods combat).

What you should know about game speed & gods animations:
- like I said in my last post, it seems that the game remains slightly faster than it should even with that fix (though not game breaking) thus at 90% speed, gods animations may seem slightly slower than it should. I'm not sure it means that we could find a better fix to make it roughly 100% correct. The game was broken because something was messing with the game speed limiter (apparently recording devices) and it appears that once fixed, this limiter remains a bit faster than it should though not so serious. Anyway it lets you enjoy a slight turbo mode at 100% speed while not breaking the game.
- moving the screen while a god's appearing will sometimes freeze its animation for a moment but I think this was already part of the game original behavior.
- also going quickly from 100% to 90% speed while a god's appearing will do the same, again not game breaking specially if you don't change the speed all the time. Worth mentioning.
- some animations don't use any speed limiter (vanilla bug) like trading post, corral, hippodrome. Just look at them at 10% speed, pretty obvious.

muttly13: Thanks for all the details on this. I dont have any recording devices (that I know of..) but I can try to fiddle some more with the sound to see if I can get it to work. Again, thanks for your time piecing this all together. Will let you know my results.

MoMoune: By recording devices I mean any audio input device on your computer so that means any mini-jack microphone as well (I guess any computer should have one at least). On my rig it was clearly the microphone related to the default playback device.

@gif_bluehawk:

Yep, for this I'm pretty sure there's something to do with any app that is using some audio resources (Steam, Media Player, Web page, Skype, TeamSpeak, non-silent mode Antivirus, etc...).
This was really misleading for me too as my fix didn't seem to work all the time then I realized that simply closing Chrome fixed the problem. Afterwards I checked with many other apps while the game was running and it seemed pretty obvious that the game didn't support it well.
Remember the time those Sierra games were released on Win 95/98, you were rarely playing with 36 apps running in the background like nowadays. Therefore it seems natural that they weren't built to support it.

There might be other issues which prevent the game from running fine though (most certainly related with the audio interface anyway).
Otherwise consider trying Pharaoh instead (in case you don't know it), does not have the same issues as Zeus but pretty the same feeling (I'd say a more complex gameplay which isn't a bad thing).