I'm not reproducing a crash in the intro with default settings in 0.74 or SVN. The invalid link state error can be avoided with umb=false, but that might not be related to the crash you're encountering. I installed from the floppies, so perhaps you could try the same in case you have a bad archive or something.

I can confirm umb=false fixes the "Invalid link state 5800 when reconfiguring MCB chain" error, but the other issue continues. DOSBox either closes shortly into the intro after the display of an "Exit to error: Illegal GRP4 call 3" message, or hangs at the same location.

I also installed off disks. Not sure if my install is different. Here's a rundown of my post install /w sound disabled "STUNTISL" content, hopefully the sub-folder content isn't relevent...

06/21/2011 11:07 PM <DIR> VAULT
06/21/2011 11:07 PM <DIR> SETS
06/21/2011 11:07 PM <DIR> RES
06/21/2011 11:07 PM <DIR> PILOTS
06/21/2011 11:15 PM 3 GAME.CFG
09/24/1992 12:00 PM 10,625 DRIVER1.BIN
09/24/1992 12:00 PM 7,898 DRIVER2.BIN
09/24/1992 12:00 PM 1,152 PFONT.BIN
09/24/1992 12:00 PM 6,462 VDATA.BIN
06/21/2011 11:07 PM 631 INSTALL.CFG
06/21/2011 11:07 PM 46,347 INSTALL.EXE
09/24/1992 12:00 PM 103,247 MAKEONE.EXE
09/24/1992 12:00 PM 102,703 PLAYONE.EXE
09/24/1992 12:00 PM 249 SETINFO.BAT
09/24/1992 12:00 PM 15 SETUP.BAT
09/24/1992 12:00 PM 137,240 STUNT.EXE
09/24/1992 12:00 PM 28,411 TYPESET.EXE
09/24/1992 12:00 PM 14,693 DRIVER3.BIN
09/24/1992 12:00 PM 266 PRINTSET.BAT
09/24/1992 12:00 PM 36,459 ADDSNDS.EXE
16 File(s) 496,401 bytes

You didn't install with official 0.74 judging from the date stamps. Installing outside DOSBox or using unofficial builds isn't necessarily a problem in this case, but it's best to remove potentially problematic elements as much as possible.

So you've tried disabling sound in the setup. What control option did you select? Also, have you tried using all default settings in DOSBox?

So, I now realize one can "esc" out of the intro and get into the game avoiding the crash, not sure if it reoccurs in later 3d portions. I'm still interested in any feedback folks can provide related to this issue though. Some additional details/queries...

Can the "Illegal GRP4 call 3" error shown in the console be explained further?

The directory listing was taken from a standard windows command prompt, which enabled cut-n-paste. I have installed under .74.

I had used the Joystick option (i.e. /wo throttle), but have now also tried the keyboard/mouse options to no effect.

I mount/run with...
mount C "U:\DOSBox\Stunt Island"
cd STUNTISL
STUNT

My config /w comments removed, which I believe aligns closely to the default is shown below.
[sdl]
fullscreen=false
fulldouble=false
fullresolution=original
windowresolution=original
output=surface
autolock=true
sensitivity=100
waitonerror=true
priority=higher,normal
mapperfile=mapper-0.74.map
usescancodes=true

[dosbox]
language=
machine=svga_s3
captures=capture
memsize=16

[render]
frameskip=0
aspect=false
scaler=normal2x

[cpu]
core=auto
cputype=auto
cycles=auto
cycleup=10
cycledown=20

[mixer]
nosound=false
rate=44100
blocksize=1024
prebuffer=20

[midi]
mpu401=intelligent
mididevice=default
midiconfig=

[sblaster]
sbtype=sb16
sbbase=220
irq=7
dma=1
hdma=5
sbmixer=true
oplmode=auto
oplemu=default
oplrate=44100

[gus]
gus=false
gusrate=44100
gusbase=240
gusirq=5
gusdma=3
ultradir=C:\ULTRASND

[speaker]
pcspeaker=true
pcrate=44100
tandy=auto
tandyrate=44100
disney=true

[joystick]
joysticktype=auto
timed=true
autofire=false
swap34=false
buttonwrap=false

[serial]
serial1=dummy
serial2=dummy
serial3=disabled
serial4=disabled

[dos]
xms=true
ems=true
umb=false
keyboardlayout=auto

[ipx]
ipx=false

The directory listing was taken from a standard windows command prompt, which enabled cut-n-paste. I have installed under .74.

If you had installed in an official 0.74 build, the date stamps on the files would be current, not the original stamps from 1992. The DOS function call that changes date/time stamps on files is not implemented in official DOSBox, although it is implemented in some unofficial builds. But again, the installation process is not necessarily the source of your problem.

The error message means an illegal instruction was encountered by the CPU. It's usually, but not always, a sign that a program has left intended execution paths (i.e. crashed).

Not sure what else to suggest. Perhaps others will be able to reproduce the problem. Although it seems unlikely that this kind of problem could result from host environment factors, I guess it's not unheard of.