@Lawrence: tab "Tasks" show no tasks at all, it is just empty, even if I click "Show all tasks" button. Tab "Projects" shows single line with the following data:
Project: World Community Grid
Account: katoda
Team: Poland
Work done: 3027750.00
Average work: 3433.32
Resoure share: 100 (100%)
Status: empty
Of course the project is not suspended.

@KWSN - A Shrubbery: the profile for this device has the following options:
Use no more than: 8 Gigabytes of disk space
Leave at least: 2 Gigabytes of disk space free
Use no more than: 80 % of total disk space
I doubt if the space is a problem, just before the crash the disk usage was almost similar and BOINC client was able to download workunits without any problems.

I'm sure that this setting is applicable only to BOINC: BOINC data cannot use more than 80% of disk space, it does not matter how many other files are on this disk. The only limit, set in device profile, is to have at least 2 GB of free space.
BOINC was working witch such usage for months without any problems.

Just to prove it, I moved BOINC data folder to another partition and here are the messages:
12/04/2012 14:28:48 Processor: 4 GenuineIntel Intel(R) Core(TM)2 Quad CPU Q9550 @ 2.83GHz [Family 6 Model 23 Stepping 7]
12/04/2012 14:28:48 Processor: 6.00 MB cache
12/04/2012 14:28:48 Processor features: fpu vme de pse tsc msr pae mce cx8 apic sep mtrr pge mca cmov pat pse36 clflush dts acpi mmx fxsr sse sse2 ss htt tm pni ssse3 cx16 sse4_1 nx lm vmx smx tm2 pbe
12/04/2012 14:28:48 OS: Microsoft Windows Vista: Ultimate x86 Edition, Service Pack 2, (06.00.6002.00)
12/04/2012 14:28:48 Memory: 3.25 GB physical, 6.69 GB virtual
12/04/2012 14:28:48 Disk: 30.10 GB total, 24.65 GB free
12/04/2012 14:28:48 Local time is UTC +2 hours
12/04/2012 14:28:48 NVIDIA GPU 0: GeForce GTX 280 (driver version 29610, CUDA version 4020, compute capability 1.3, 1024MB, 622 GFLOPS peak)
12/04/2012 14:28:48 World Community Grid URL http://www.worldcommunitygrid.org/; Computer ID 457589; resource share 100
12/04/2012 14:28:48 World Community Grid General prefs: from World Community Grid (last modified 11-Apr-2012 23:45:36)
12/04/2012 14:28:48 World Community Grid Computer location: work
12/04/2012 14:28:48 General prefs: using separate prefs for work
12/04/2012 14:28:48 Preferences:
12/04/2012 14:28:48 max memory usage when active: 2494.59MB
12/04/2012 14:28:48 max memory usage when idle: 2993.51MB
12/04/2012 14:28:48 max disk usage: 8.00GB
12/04/2012 14:28:48 don't use GPU while active
12/04/2012 14:28:48 (to change preferences, visit the web site of an attached project, or select Preferences in the Manager)
12/04/2012 14:28:48 Not using a proxy
12/04/2012 14:28:59 World Community Grid update requested by user
12/04/2012 14:29:03 World Community Grid Sending scheduler request: Requested by user.
12/04/2012 14:29:03 World Community Grid Requesting new tasks for CPU and GPU
12/04/2012 14:29:06 World Community Grid Scheduler request completed: got 0 new tasks
12/04/2012 14:29:22 World Community Grid Sending scheduler request: To fetch work.
12/04/2012 14:29:22 World Community Grid Requesting new tasks for CPU
12/04/2012 14:29:24 World Community Grid Scheduler request completed: got 0 new tasks

So now BOINC has plenty of free space and it does not change anything.

And do not worry, this is not my system disk, but other, called "Storage", when I keep other stuff :)

Just for your information, after hours of searching for any information on various forums, I decided to wipe all BOINC data folder content and then re-attach BOINC client again. Right after that I received new workunits and since yesterday my quad core machine is happily crunching. Looks like during the crash something wrong happened to one of the files and this prevented BOINC client to get work to crunch.
I was lucky, as nothing changed in my hardware/software setup, BOINC server gave me my previous device ID, so I avoided my biggest problem :)