So can you get as far as an init3 (command line) login where you can insert your username or password without a window manager (kde or something) starting ? because I've got an idea that you'd have to get to that stage to be able to look at the log's to see what the error or problem might be?
If you can, do the login and try ls /var/log which should show which log's are available to look at (sorry I don't recall, but after the log in, if it tell's you that you can't see the log's as user then you might have to either log out and back in as root or just "su" to root - it'll ask for the root password).
bash-2.05b$ ls /var/log
auth.log explanations.5.gz nvidia-installer.log syslog.2.gz
auth.log.1.gz kernel rpmpkgs syslog.3.gz
auth.log.2.gz ksyms.0 rpmpkgs.1.gz syslog.4.gz
auth.log.3.gz ksyms.1 rpmpkgs.2.gz syslog.5.gz
auth.log.4.gz ksyms.2 rpmpkgs.3.gz urpmi.log
auth.log.5.gz ksyms.3 rpmpkgs.4.gz urpmi.log.1.gz
boot.log ksyms.4 samba urpmi.log.2.gz
boot.log.1.gz ksyms.5 scrollkeeper.log urpmi.log.3.gz
boot.log.2.gz ksyms.6 secure urpmi.log.4.gz
boot.log.3.gz lastlog secure.1.gz user.log
boot.log.4.gz lastlog.1.gz secure.2.gz user.log.1.gz
boot.log.5.gz lpr secure.3.gz user.log.2.gz
cron mail secure.4.gz user.log.3.gz
cups mdkkdm.log secure.5.gz user.log.4.gz
daemons messages security user.log.5.gz
dmesg messages.1.gz security.log wtmp
explanations messages.2.gz security.log.1.gz wtmp.1.gz
explanations.1.gz messages.3.gz security.log.2.gz XFree86.0.log
explanations.2.gz messages.4.gz spooler XFree86.0.log.old
explanations.3.gz messages.5.gz syslog XFree86.1.log
explanations.4.gz news syslog.1.gz
bash-2.05b$ ls /var/log/syslog
bash-2.05b$ vi /var/log/syslog
+ Stopped vi /var/log/syslog
[root@johnspc john]# vi /var/log/syslog
If you look at the bit I've quoted, it show's that I can list the various log's from the $ (user) prompt, but when I try to look at the syslog using the "vi" editor (the vi /var/log/syslog bit) it told me that permission was denied so I had to su to root and then it let me look at it.
I don't know which log any error's might show, but some are obvious (like the spooler - as that's to do with printing, so it's unlikely that you'd find any error's showing unless they're printing error's etc etc).
As you say the system is hanging I'm presuming that you can't enter a graphic environment and use, say the kwrite editor to look at the log's. Hence I used vi in my example cos I know it's installed by default in mandrake, but which ever way you will probably need to have a quick surf to find the basic command's (cos window's is crap and won't let you look into linux, whereas you can look at windows from linux).
Sorry if that sound's a bit confusing, but I can't think of anywhere else too look for error's to see why your system might be hanging!