1998 Honda Civic won't start on own

I was thinking a few months ago my battery was starting to
go out on me. My car seemed to struggle to start, like no
power. I had it running one day and unhooked the battery
and the car still ran, so I assumed the alternator is good. So
I replaced the battery about a  month ago and have only
driven once or twice since then (the car is basically a spare
vehicle). I went to start it last night, the dash lights all came
on no issues, until I turned the key. It was dead. I put my
battery jump box on it and it fired up. When I turned on the
headlights, the radio turned off and back on. Drove to the
store with no problems and parked. Came out after ten
minutes,  same thing. No start. Used the jump box and fired
right up. Drove the 5 miles home with no issues and let it sit
and run for 30+ minutes. After all that time I tried the
headlights and again, the radio went off and came back on.
I also noticed the lights dimming when doing that. Before
parking it, I turned everything off and then hit the high
beams and defroster at the same time to see what would
happen. As expected, the headlights dimmed way down
and the car died. And would not start. Acts as though the
battery is dead. It seems like it cannot handle the rush of
current from turning everything on, but also cannot start on
it's own. No sound system,  no extras, just a stock 22 year
old Civic with 207k miles