I have a new battery and alternator and it ran great than after forget something i tried to start it and clicked.. so i jumped it let it run but as soon as I turned on the lights it died

I just bought the battery Wednesday... I've drove around and everything.... every thing was working right.... then I just got back to the house and forgot something and tried to start it right back up and that's when it happened... then after jumping it it started immediately and I ran it for like 15 minutes and noticed I didn't have a radio or the air blower was not working... so I tried turning on the lights and it immediately died.... my positive cable does need to be replaced... but IVE always thought if there is still a connection it should work... where else could I look to see why its doing this... I drove it around for like almost 4 days before this happened.... the motor is still running great and quiet... how can I check the voltage... I remember when I was younger that if you took off the positive cable... if the vehicle stayed running it wasn't the alternator... if the car died than it was... but I don't know if my vehicle is to new to do that as a test... I bought the battery Wednesday at Walmart and it's the battery that goes to the vehicle... I had it looked up