repair or replace pvc connection?

My question concerns the drain pipes underneath the kitchen sink. We've lived here for 5+ years and recently because of a back-uped sink I disassembled the confusing mass of PVC pipes/joints and cleaned them out,they were dirty but not clogged. After reassembling the pipes we've now noticed that there's a slow leak where two pipes are fitted together and the drain is still backed-up so the clog is farther down the line than we thought.
What would be the best solution to stop the pipe from leaking for a very untalented handyman? Also, does anyone recommend the standard clog removers Vs the newer "powerful forced air" drain cleaners? Thanks in advance for any and all of your help. ps I really do mean it when I say I'm an UNTALENTED handyman so please reply with easy instructions.

You only have to replace the PVC if the pipes are damaged. Is your leak coming from 2 pipes that are joined with a threaded connection? If yes, then use some pipe thread compound on the threads. It seals the threads and keeps them lubed for future removal. This compound works better than teflon tape which I've found works better on metal threads. TIghten the nut by hand 'fairly tight', and turn on the water. Turn it tighter by hand until the leak stops. If you've tightedned as far as it'll go, use a wrench to gently tighten 1/4 turn more. Don't do more than that, bkz you'll damage the threads, and then you'll have to replace the pipe.

I haven't used the air jets, but I have used a pipe snake with success. They're like big, fat, floppy gentle drill bits that you turn by hand or with a drill to dislodge debris deep inside a pipe. Use the pipe snake with the trap and as much of the drain dismantled as possible, so you don't have too many bends to navigate.

Don't waste you time and money with chemicals. They will not work and will create a potential hazzard. DIY snakes are often not effective because they are too small. I fear the air jet idea would just push the clog deeper and tighter. The best thing to do is realize that some things are better left to the pros and call a plumber that can properly auger the drain.