Some things to try
1.) Use NTVDM's Dos sound emulator. It has not been updated in AGES, but it works for almost all DOS games that I have tried under XP.
2.) You may have to call it quits when it comes to playing the windows version. The windows version was coded in such a way that it tries to directly access hardware resources. Something which the NT architecture (XP is an NT-based OS) will not "allow".
3.) Westwood is going to release ALL the C&C / Red Alert / Generals games that they have created so far in one megapack. Obviously they are NOT going to do this knowing that the older games will not run on XP, so I expect they might bundle some sort of solution along with it. Perhaps you might want to look into that?
4.) Look at some community spots that sport old strategy games like C&C / Red Alert. I can gurantee you someone else is having the same problem as you do, and has discussed it in such community areas. They might even have some sort of "patch" or "loader" that can start the game under XP?
5.) Read the NTCompatible.com Compatiblity profile for this game (Red Alert 1). You might look into the comments that users left. Someone may have already figured this out?
This says tested under NT4, but you never know. It may work under XP -->
Works Under NT4
This is a guide to getting it to work under Windows 2000. Since XP was built from 2000, I would not be surprised if you cna get this to work for you -->
Works under 2k
this is a painful solution but might work for you -->
Install under Win9x/Me first
I hope this helps