Troubleshooting the central air conditioner compressor?

As in most of the country, it was terribly hot and humid in the semi-desert today. The air conditioner was working fine at the beginning of the day, and later in the afternoon, it wasn't blowing cold air. So I hope to solve this problem before I call the HVAC staff.
I never hear the compressor turn on, but the fan is running. Inside my device, I have a single trigger capacitor. When I watch the video and instructions for replacing the air conditioner condenser, it seems that if one unit fails, both the fan and the compressor stop. Since my fan is running but there is no compressor, can the condenser still be bad or do I have another problem?

I think your filters are dirty. Try to change it

You need to change fancoils. Usually it helps

It's summer soon, but it's totally not my favorite season of the year. I withstand cold better, than hot, so I prefer autumn and winter more. On summer hot days I use air conditioner really often. Actually I had an accident with my aircon recently. It didn't work well, so my elder brother decided to check it by himself. As a result he was electrocuted, but he's fine. Nothing serious.

Oh, really? I've almost the same story, but with my grandfather. Sometimes he's too confident, and it ends up not really good... We change filters in our air conditioner every six months. Usually it does my dad, but in that day he was at the business trip. Happily, my grandpa didn't get electrocuted, but he was quite nervous he couldn't open aircon's cap. After all, he decided to call guys from https://www.airconservicing.org/why-choose-us/. They changed filters and a fancoil. A/C worked even better. That's why I don't like to fix something by myself. Electricity is no joke. Be careful guys.