Yup, agree with Petrusclavus, it is an alternator problem. You can usually take the battery back to the place you got it and they will charge it, this should start the car and you can then use a volt meter to see if the system is charging. The battery by itself should test at just over 12 volts. When the car is started you can test the battery again and should see it test at 13 or low 14 volts, meaning the alternator is charging the system. If you do not see this change it is your alternator.
Check all the connection from your battery post to the starter and to the ground for good connection and check to see if the cable is in good condition.
GL
Get a voltmeter. Jump start the car and measure the voltage between + and - on the battery. With the car running and the alternator working, it should read about 14 volts. If it is less than 13, your alternator isn't charging the battery. If the alternator is working, you may have a bad replacement battery.
clearly it means it's not the battery that's the problem. Tow it to the shop and have them do one of those electronic tests on the car to see what else could be the problem.
Alternator/charger fail - it was not the battery at fault.
When you have a flat battery ask WHY the battery is flat.
The new battery flatted while driving, earth short, alternator broken - plenty of possible causes.
Sounds like a problem with the ignition switch as it started the second time. Check all connections as well to make sure they are tight.
Ignition switch or starter solenoid needs to be replaced.
My car started to crank slowly recently, so I had the battery tested. It was almost out of juice, so I thought I would replace it before I get stranded. I put the new battery in and it started right up. Took it for a drive and was fine. I got back in the car, turned the key and nothing. Tried it again and started right up. Go back to the car for work and nothing at all. No cranking. Just a slight click and that's it. No matter how many times I try it won't start. Put the old battery back in and same thing, doesn't start. Dash lights and radio go on though.