I had one thought that hasn't been covered. Your computer has a small battery on the motherboard that is supposed to last about 4-5 years. If this battery runs down, the date/time will not be stored. This is a long shot though, as I cannot remember the last time I had this problem - 8 years?
So, if the solutions above do not work, and especially the great suggestion to create a new user, the only recourse left (and it may be a good idea under the circumstances**), is to perform an clean reinstallation of your system.
I presume you have your 10.6.x disk. Make a clone (I like Carbon Copy Cloner) to an external drive, or a complete Time Machine backup.
1.Reinstall Snow Leopard.
2.Check / repair permissions as many times as necessary.
3.Perform Software Updates as many times as necessary.
4.Repeat step 2.
Let us know the outcome. Good luck.
** if there is something screwy with the date and time prefs, then other system functions may also be malfunctioning, and you don't want to end up with bad/missing data.