If you took it back, they will just plug it in and show it working, with you then left trying to explain that you think it has an inherent fault, which is also reported by others online.
I also suspect that they will say that different monitors have slightly different performance levels and the one you bought may not be suitable for the usage required by you. If they did not advise you on which monitor to buy and they have not failed to describe performance spec accurately, then I can see them swapping it for another.
What I would do if I were in a position of a store not helping, is to threaten to involve Trading Standards if they cannot resolve, Tell them you think the monitor has an intermittent fault, with the performance issues you described. Intermittent faults can be very hard to prove and if you only bought the monitor recently, I think you can return it to the retailer for a full refund within 6 months of purchase. If you say intermittent, even if they plugged it in and it did not show a fault, they might just take your word for it. They might offer you a replacement for the same make/model, but I suspect you can ask to replace it with another make/model paying any extra required if it costs more.
http://www.direct.gov.uk/en/Governmentcitizensandrights/Consumerrights/Yourconsumerrightswhenbuyinggoodsandservices/DG_194650