I had this problem with a monitor too and as a previous poster stated I got an old/ bad looking 2nd hand replacement...which also had a lit pixel.
This really annoyed me ...so erm...I lied.... I had also lied the first time.
I phoned them back and said that the replacement had 6 pixels...1 lit one but 5 unlit.
I actually did this ...wait for it 5 times...each monitor got worse and older than the last until my 6th monitor had 300 dead pixels!!! Well a vertical line of lit pixels from the bottm of the screen to about a third of the way up.
After this and a bit of hassle my 7th monitor came straight from head office and was brand new with no dead pixels.
This was only possible due to the company operating a collection and replacement policy.
I know it was wrong to lie but if I had gone to a shop and looked at a screen and noticed a lit pixel I wouldn't have bought it.
I'm not advising you to do the same but that was the way I got mine sorted.