Don't worry. I built tonnes of pc's and i always used the bar minimum of screws necessary.

CD-ROM/Hard drive: 1 screw
ISA/PCI cards: no screws
Chassis: no screws
COM/LPT/VGA port cables: no screwing

The worst that ever happened was that maybe once or twice a cable came loose and only once when i tried to plugin my vga cable in the videocard that it came loose from its pci slot. Fortunately because i had no screws on the chassis either that was fixed in a minute.