No need for explosives (unless you fail...)
First, you CAN swap motherboards and have your system come up. I have done it quite a bit (I do PC tech work plus I have 6 PCs at home). I'll try to keep this short. You didn't say what OS you have but I'll assume some flavor of Win95/Win98. Win98 has improved plug-n-pray so it is a bit easier but things will also work under Win95. First thing is to back up your hard drive if possible, at least your critical files. Next thing to do BEFORE swapping is if you are using any sort of special IDE disk driver (sometimes called "Bus Mastering driver") you want to unload it, since your new board will be different. You do this through control panel. Then power down and swap your board. When you boot up, immediately go into the system BIOS (usually done by hitting the DELETE key). You will find a utility for "autodetecting" your IDE hard drives. Run that and make sure it sees all hard drives. Then manually configure floppie drives and time of day. Finally look for a BIOS setting that indicates whether you have a Plug'N'Play operating system. Make sure that says YES. Then save settings and restart the system.
If everything is cool in the BIOS the system will boot. It may seem like all hell is breaking loose because you will see a bunch of messages that Windows is finding all kinds of hardware. This is because the IRQs and addresses of your plug'n'play hardware will be different. Most likely you will not need to re-install any drivers because they are already there, the system will just shuffle the hardware settings. Just in case you may wish to have the hardware driver disks handy. After a while it will finish and everything should be fine.
As to your second question, AT motherboards are somewhat square and rarely have any ports directly on them except the keyboard - serial and parallel ports are connected by wires to a slot cover or port. ATX motherboards are very rectangular and have parallel/serial/keyboard/mouse ports all poking directly out of the case. The power supply connections are different too, so you can't put one kind of board in the other kind of case. However cases are cheap - $30/40 for a ATX mid-tower case.
Hope that answers your questions and good luck.