Problem accessing one website on iMac

I have been using a Vons online grocery delivery site for years. They changed their website a month ago and ever since then I cannot get onto that one site. It is the only site I cannot access. I can sign on and enter password, but then get a spinning wheel and that is the end of that. I have called and emailed them many times and they suggest I try to clear my cache and cookies/restart etc. I did that plus reset Safari and flushed my DNS...which I don't even know what that means.........and to no avail. One of the people I spoke to thought perhaps it was due to my still using Mavericks and suggested that I upgrade to newer OSX. Since I have 2011 or 2012 computer I think that boat has sailed. I refuse to purchase a new Mac just to use one website either. Note: I am able to use the site via my iPad, but that is not as convenient. So, the site works, just not from my desktop computer. Any thoughts? I am no computer wiz. which may be obvious. Thanks.