There was much rebellion, both against the ruling Welsh lords, eg of Gwynedd, and against the local powerhouse of the English Crown. Edward I conquered Gwynedd by bringing Llywelyn ap Gruffudd ("the Last") under his boot and so imposed the power that Gwynedd previously held over large swathes of [what we now call] Wales.
Then the lands of "Wales" were annexed, this annexation taking various forms but certainly meaning that the lands of Great Britain to the West became a part of England (brought in to certainty by Henry VIII, whose ancestors were subordinates of the aforementioned rulers of Gwynedd).
So yes, a country can be many things, but it seems it needs something more than just geographic locality to be worthy of calling a country: "Wales" which we now know is an amalgamation of counties of the English crown won over a period of a couple hundred years from various rulers. It's a country in the same way that "Wessex, Sussex, Kent and Wight" is a country, an arbitrary grouping of a largely historic county regions based on locality - actually that's got a greater claim to be a country as it's the historic Kingdom of Caedwalla whilst "Wales" seemingly was only united as an administrative regional grouping of counties whose lords had been brought under fealty of the King of England. Long before that it had lost any unity of identity when the Romans, "Irish", Vikings and others came and pushed around the Celtic and Britthonic speaking people's who'd been there prior to the CE.
So I can accept Powys as a country, or Gwent, or Gwynedd, but Wales never really seems to have been a country until ... well I don't know, but I think since 1964?? The Acts of Union were between the countries of England and Scotland and Ireland. The Council of Wales, like the Council of the North, was abolished in the mid-17th Century in favour of direct government from London ... "the country of Wales" seems to be a pretty recent invention.
Looking at the more recent history of the 'electoral regions of England known as Wales': the Eisteddfod is seen as long standing historic event that epitomises the independence of Wales as a nation but it dates from the later half of the 19th Century and the druidic pomp of the Gorsedd seemingly has no historical basis other than being the invention of a London based academic in 1792; hardly the pre-Roman druid roots that people imagine the Eisteddfod as having when they see the gowns, the throne, and the sword (eg http://www.museumwales.ac.uk/articles/2010-07-25/Scrolls-swo..., http://www.bbc.co.uk/guides/ztbk87h).
Hence the question: When did it become a country? Or if you prefer more specificity: When did the region of land we today call "Wales" acquire any sort of significant unity of governance, as a totality, separate from England?
[It's amazing how tribal reach thousands of years ago, eg of the Silures, brings to bear on the nature of nationhood today. As you perhaps can tell this is a subject I find quite fascinating, encompassing as it does so much of British history and modern politics within such a small question.]