Very unusual problem with computer, please help

You may be a vctim of static electricity,its far more serious then you may think. Find the part that you touched the most  

Thanks, but usually when I clean all parts I touch them all, and as I've written before it works perfectly but only when case is lied on the table, if I put it back normally still freezing. I'll try to make selective boot for a moment....

Sounds like your motherboard is shorting out on your case somewhere, check for standoffs in wrong place, loose screws floating around.

Had the same problem when switching cases. As pgooch pointed out check for a short, but what has also served me well is clearing the cmos.

When you reassemble your case, insert the power supply first, then the motherboard (don't connect any cables yet), but leave the screws "slightly loose". Insert your cards and screw them to the case - making sure each lines up correctly. The motherboard should move slightly to allow for adjustments.

After the cards are all seated, and everything is aligned, tighten the screws on the motherboard. Then connect the cables (you may have to remove a card to get this done.

Often, either the motherboard is not aligned properly, or the stress of a card moving the motherboard when inserted creates this issue.

If everything doesn't align perfectly, check the standoffs for the motherboard - make sure that none are "bent" (out of perfect 90 degree alignment), check the case to make sure it is "plumb" (meaning perfectly square).

If you are breadboarding it and it works, it has to be something in the alignment of the mobo/cards that is creating the problem....

I cleared CMOS couple of times, and problem persists, but there's no problem if my case lies on one side, it boots, and works normally like before. I'm going to change screws and front panel cables. Perhaps it'll help. Thanks

If you are looking for a suspect cable, it's quicker to just move each suspect cable, one at a time, until you get a reaction.

I have seen systems that had very flexible cases and would not work depending on how you picked them up. The time I am thinking of if you picked up the case from opposite corners, the whole case would flex and PCI cards would pop out of their slots slightly.

I would set the machine up and push on the components to make sure they are seated correctly, then power up. (after checking for devices that could be shorted to ground. (or unplug stuff until you get power to the motherboard)).