HoMM3 HD is a mod (add-on) for the game Heroes of Might and Magic 3.

Event name: APPCRASH
Application name: Heroes3HD.exe
Application version: 3.2.0.0
Application timestamp: 31313931
Fault module name: MP3DEC.ASI
Fault module version: 3.0.0.0
Fault module timestamp: 36910efa
Exception code: c0000005
Exception offset: 000076f1
OS version: 6.1.7601.2.1.0.768.11
Language code: 1049
Additional information 1: 0a9e
Additional information 2: 0a9e372d3b4ad19135b953a78882e789
Additional information 3: 0a9e
Additional information 4: 0a9e372d3b4ad19135b953a78882e789

Is this issue only present without HD?

Option 1: Enable compatibility mode with Windows 98 in the properties of the executable file.
Option 2: Turn off the sound in the game, i.e., move the music and effects sliders to the minimum.

Please let me know if either of these solutions works.

Added 1 minute ago
By the way, I'm still too lazy to install Windows 7 and only test on XP.
In the future, I will try to find time to test on Windows 7.

Added 3 hours 10 minutes ago
I played Complete Eng vs SoD Eng over the network on XP for an hour - no problems were noticed.