I've got same symptoms: on dosbox 0.7, it hangs on any dialog box. Only when sound and music are disabled, the game works.

The simplest way to hang the game is to start new campaign and press "Esc" - it hangs on the exit confirmation dialog.

I'm usign image of the X-com CD, my "music" file has 311 689 216 bytes. I have a strange feeling that this bug has something to do with the music file, but since there are no separate settings for music and sound, I cannot be sure - I can't disable music when keeping sounds.

I'm using the CD patch (without it, the game don't want to start), but I'm not mounting CD as patch says (it says to use fakecd), but in more Dosbox-way; this is my batch to execute game:

1mount d l:\ -t cdrom -usecd 2
2xcom3_cd.com
3xcomapoc.exe SKIP

I made it work "better".

What to do to make the game work:

- Create a directory for the game
- Inside this directory, make a file "play.bat" containing:

1@mount d l:\ -t cdrom -usecd 2

(use your CD letter and correct number in -usecd switch)
- Create a shortcut to run the game:

1dosbox.exe -conf dosboxXCom3.conf -c "mount c d:\games\X-COM3\ -freesize 400" -c "c:" -c "play.bat"

- insert game CD, run the shortcut, in DOSBox type:

1d:
2install

- Install the game into C:\ (note that it will install in the directory you mounted, not in real C:\)
- Download xcom3_mousefix.rar, x3svga.zip and the latest dos32a
- place XCOM3_XP.EXE from xcom3_mousefix.rar in the game directory. This patch is a Pascal program which merges no-cd patch and mouse patch.
- edit your "play.bat" file and add at its end:

1XCOM3_XP.EXE xcomapoc.exe SKIP
2exit

- extract x3svga.zip, copy tacpPatch.exe and ufo2pPatch.exe to the directories where TACP.EXE and UFO2P.EXE are located. Execute the patches.
- Extract dos32a. Copy both TACP.EXE and UFO2P.EXE to the directory wher dos32a is extracted.
- Open a command prompt in that directory and type:

1sb /U TACP.EXE
2del TACP.EXE
3sb /B TACP.LE
4sb /U UFO2P.EXE
5del UFO2P.EXE
6sb /B UFO2P.LE

- Overwrite the original TACP.EXE and UFO2P.EXE with the ones that have been created with "sb.exe".

..And play.

Still remains a problem: mouse goes too fast; but the game should work quite stable.

Update: I see it still hangs, but now the game seems to continue working, only keyboard/mouse controls are disabling.

Anyway I think I tried everything, and it won't work. I tried:
- applying all patches I could find
- changing DOS4GW in all EXE files (PLAYER.OVL, TACP.EXE, UFO2P.EXE, SMKP.EXE)
- updating HMI sound and music drivers
- disabling music and sound via in-game menu (not in SETUP)
- changing DOSBox configuration in many ways

After some modifications, game works little bit longer, but mouse and keyboard always stops, sooner or later.

Conclusion: X-Com Apocalypse (at least the version I have) won't run correctly under dosbox 0.7 with sound enabled. The only way to make it work is to disable sound card via setup.

Does it work if you set core=normal? Does loadfix change something?

I tried normal core, but it has no effect.

I didn't tried loadfix.... now I've deleted all the game files, so I lost my chance of checking it.

Actually I set-up Windows 98 on my old P2 Celeron machine, and now I'm playing natively. Only switching the monitor cable with the "real pc" is a little bit anoying.