Whoa horse.
Let's take this one step at a time. First of all, turn off the com ports again, unless you need them.
Next, the reason for moving the cards is to get them one their own IRQ, in other words, not sharing with something else. This is a logical step by step process since most motherboard manufacturers don't disclose this information in te manual.
On motherboards, some PCI slots share IRQ numbers. For example, slot 4 and 5 might share an IRQ. So if you plug in a modem in slot 4 and a sound card in slot 5, their going to use the same IRQ. You will be able to change the number, say from 9 to 11 or 7, but the two cards will always be the same number. In other words, they will both be 9, or they will both be 11.
Another sharing problem is that some PCI slots share IRQ's with onboard devices. For example PCI slot 2 might share an IRQ with an onboard Ultra 100 controller, and PCI slot 3 might share and IRQ with an onboard USB controller. The same goes for these. You can change the number that they use, 9, 7, 11, but they will always share the same number.
Luckily, the motherboard gods always give you at least one PCI slot that doesn't share an IRQ. Most of the time you get more than one. Since you don't know which one(s) it is, you have to use trial and error by plugging your cards into each slot one by one and then booting the computer to see which IRQ it grabs.
So...
I would try to find a PCI slot for your decoder card that doesn't share an IRQ.
You can also try and update all your software, video card drivers, DVD drivers, etc. I'm not so sure the problem is IRQ related. It might be, it might not be.
Now that you described the symptoms a little more, it reminds me of the time when a certain release of drivers for my video card wouldn't play DVD movies. Sometimes my computer would restart too. When NVidia released new drivers, the problem went away.