Okay thank you for confirming.
Unfortunately, the issues you are experiencing are symptomatic of an internal hardware defect, meaning a faulty power supply or logic board. This issue could be a manufacturing defect, but is also often caused by a power event (shock/surge, prolonged over/under voltage condition, etc).
This could also be the result of age related wear and tear, as a 2008 model, that type of failure wouldn’t be surprising as this machine was designed and built for only a 3 year service life.
These lexmarks are widely regarded as the worst printers ever made, they were very poorly designed and built and have very high failure rates. They were so bad that lexmark nearly went bankrupt supporting all the warranty claims, and stopped making inkjets entirely shortly after this model.
There is one step you can take here, both as a possible fix, as well as a diagnostic evaluation
unplug power at the wall outlet
wait 5 minutes
press and hold the power/on button for 60+ seconds
keep holding while plugging back in, and for another 60 seconds after, then release
If this reset process does not work, it would unfortunately confirm an internal hardware failure.
This is something that would require repairs to correct; at that point it is time for a new printer. While it can be fixed, it is not practical to do so. You'd be in the $150 range to have the internal power supply, and a logic board would run you $200-250. For $80-100 you can replace the entire machine with a brand new model, with current technology and a fresh warranty, which makes more sense than buying the new part for an older printer.
Depending how you'd like to proceed, I can help with finding parts, finding a local repair shop, or recommending replacement options for you. Just let me know.
Best regards, ***** ***** for the news,