DIAGNOSIS You're describing panel uniformity issues common to VA panels: backlight bleed (white glow) in corners and VA glow/darkening (dark smudges), which are inherent to the technology, not dirt.
FIX First, reduce the monitor's brightness from the default 100% to a more reasonable 60-80% for normal use. High brightness exaggerates these effects. Check uniformity on a mid-gray test image, not a pure black screen.
IF THAT DIDN'T WORK Gently massage the affected corner of the bezel with your thumb while the screen is off. Sometimes pressure from the bezel assembly can cause shadowing, and this can temporarily alleviate it.
HEADS UP Some degree of corner glow or shadowing is normal and within manufacturing tolerance for this panel type. It's only considered a defect if it's severe and visible during normal content viewing, not just on test patterns.