Some newer window A/C's have a built in delay timer, 2-3 minutes, so a small delay is common.
This time of the year there will be loads of sales on window units. I'll bet that for less than $100 more you can buy a new 24,000 on sale.
IMHO, The price of used things are over priced. I once bought a used trailer. By the time I got it all fix, wired, new tires, brakes, lights, painted it was close to the price of new and I had a 15 year old trailer.
Bought a Jubilee, by the time I got it fixed up have twice the money in it than I can sell it for.
The same with cars and trucks. I buy new cars and trucks when next years models come out. My Car and truck were discounted about 30%, which was close to what used was selling for.
Wait for sales and get a new A/C.