Before you spend any money on mother boards and other upgrades......
I did not see anywhere where you mention which sound card you are using.
The symptoms you described : "drop outs" are typical sound card issues and tend to point to a factory sound card issue. If you are using X1 with a factory sound card, that could very well be the source of the problems including the BSOD. Your settings could also be playing a part in the drops. Are the drops on synths or are they on e entire project audio included? Synths would be latency settings and buffers, audio would be more directly related to the sound card itself.
If you are running X1 with a factory card, I would highly recommend the purchase of a USB based interface which uses ASIO drivers before doing any other upgrades.
While I do concur that the processor and memory should be no less than the factory recommended minimums, it is very possible to run X1 on a less than optimal computer. I have done this in the past and gotten good results. Some of the processes take a bit longer to do, but the system will usually run OK. You might not be able to run a project with 8 synths in it and a bunch of audio FX at the same time, but it will run..... just not like it would on a more capable PC.