My Hp Laserjet Pro 400 m401dn stopped working

First thing I'd do is check the power supplies (HVPS and LVPS) for issues. As far as testing goes I would not test or repair the HVPS - replace it for your own safety as there's not a good way to "test" it without exposing stuff which could hurt or kill you. The LVPS is more accessible on these. Use this SM to work on the printer: https://www.laserexpressinc.com/manuals/...

The next thing to do is try a new USB printer cable - buy a new one if you do not have another one you can borrow. Sometimes these older HP printers do that when the cable is really bad, but 7/10 times they will ignore the cable. Pray it's that.

If the issue continues with a new known good cable, then the formatter board might be bad on the USB port, but to confirm that try using the ethernet port. These do not have a WLAN card to die and bootloop the printer like the DW, but the dn (color LCD) and DNE (2 line, upgraded M401n base with the stripped down LCD option), so it's not going to be that simple. You might be able to replace the USB port at the component level to fix it, but if it's shutting down hard, it might be a deeper issue like with the RISC processor or RAM. if that's the case then you can probably get another board for it, but you need to dump the product info locally, learn HP PJL or pray there's a leaked tool HP uses to avoid PJL, or replace the printer with another low meter DN or DNE (same thing, different LCDs). There's still plenty of low meter ones out there, but they're up there 20-30k pages is the current low meter and 100k+ is well used unless you get lucky and keep looking for a gem.

That said, what I did as time got to me with mine, I bought a monochrome Lexmark to replace it when the time came - I picked up a MS621 and later a MS631 (1) which I've liked, but if you do not want a full blown commercial model, the MS/MX4 series is equally as good -- just has a shorter fuser life before it comes up to needing it at 100k pages vs 200k on the MS5 and up. I also like the color LCD monochrome Brothers with duplex scan and ADF (seriously... ~$100 upgrade) as they are easier to set to print on "empty" toner then the 1-line models, but Canon also makes solid machines.
(1) -- I picked mine up broken for scrap metal and a cheap fuser because I wanted one anyway, but couldn't bear to scrap it without trying to save it given the printer was so new it came with the SWP toner and initial 75k page drum with ZERO usage (actually 21 pages on the counter when I checked, I confirmed it in service mode as the drum had 21 cycles -- I put 2 pages on it to check the meter and it counts up). Ended up being a $0 problem and it ran fine. I wouldn't pursue a broken unit unless you are okay with 50lbs of scrap to haul being a risk, but I got an $850 printer for scrap pricing.