Warning from DOT/Shotty company equipment/Need advice

I work for a very small ltl company right now with trash equipment. Every trailer with lifts has a hydraulic leak (I reported this 3 months ago), not much gets fixed around here just the bare minimum. Well today while making deliveries my main cylinder seal blew out completely and I was dragging my lift.

Luckily I was pulled over/spotted by DOT (I think it just happened because there isn't much damage/if any scraping on the lift). He gave me a warning and told me I was lucky to not get a DOT inspection which I agreed because my truck does have check engine light and terrible tires. I asked him several times if this warning would show up anywhere on my backround or driving record and he insisted no. Can someone clear this up, will this warning show on a pre employment backround screen for a CDL position?

I don't know what to do about the job, obviously I am going to demand getting everything on my rig and every trailer from here on out fixed but I'm not sure if it's going to happen. What would you do?

Look at what the warning states in the picture uploaded, if that stuff shows up that will look super bad on my record.

 

There is a lock, but that's broken too

 

Do you know if it shows up on your DOT record/any record if looking for a new job?

 

Yes this one definitely needs one we have a couple trailers that do.

It was not on a DOT inspection report.