It's either a hardware issue or a wrong driver. Since I assume that you installed all the right drivers, a hardware issue remains. All you can do: run diagnostics (all good techs have them) or swap parts (all good techs have spare parts).
What error code and description does the blue screen mention? That might be useful to pinpoint the issue. Or totally unuseful, of course.
Doesn't your new computer have a PSU? And did you maybe overclock, or set any other than the default or recommended BIOS options?