New battery and starting troubles

I have a 2005 prius, about 170,000 miles, that’s having a bad week. I just got the starter battery replaced. Went to great efforts (no one had it in stock...) to get the right one, so I sure hope the dealer did that right. It was starting fine, just not able to sit long before dead, and the battery tested very low in amps and whatever they do to determine if a new one is needed. Ever since I got that new one in there has been funky. one thing that may be to do with it is that I ran it dead shortly after, airing it out with the back door open, because my car needs to air out a lot, as it’s been through some dirty shoes and moisture. We started it again, but now it has everyone where I live alarmed... once off, it does not start again. That has me baffled. Someone said maybe it was so dead it needs to drive for a while. Is this true? I drove it a little, and it was on, running occasionally, for 30+ minutes. Right now it does not start properly at all, behaving weirder than it’s ever behaved. Any ideas? Thanks so much
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Clarifacation
Does not start without jump. Was not starting properly as of last night even with a jump. Some connection, probably around it’s starting mechanism, was making funny noises. The screen was on, the dash was off. The dash was on, the screen was off.