Hello, Tommy;
Assuming that the electrical wiring in the vehicle is not modified in any way that could result in the blower switch feeding current into a computer input or some other strange problem like that, then the most likely cause of what you describe would be a malfunctioning charging system or a very weak battery.
If the charging system is not operating correctly, the added high current draw of the blower motor might be enough to drop system voltage down below the point where the ignition system and electric fuel pump can operate.
I would suggest using a DVOM to check battery voltage when the car is running; it should be 12.6 volts or more with the key on engine off, and should be in the 14 volt range with the engine running. If not, you may need an alternator or have other charging system problems.
I hope this is helpful; if so, an accept would be most appreciated! thanks!