Cannot Access Our Own Website Or Emails?

We updated our business website in December and moved the hosting to our web designer's servers.Very shortly afterwards, we discovered that we could not view our own website, nor access our emails, which are hosted through our web domain name via cPanel.We run two Apple Macs through a Linksys router connected by two ethernet cables. We also have a Vonage internet phone connected to the network, which works either connected directly to the modem, or routed through the Linksys.We had this set up since March and had never had any problems until we had the new website. We don't know if its related, or just a coincidence.

We first went through a process of elimination:

First we connected the computers directly to the modem (one at a time, as obviously both can't connect directly) and we could access our emails and website absolutely fine. Not a solution though, as we need access on two machines.This led us to believe the problem was with the router. Both the Linksys and the Vonage device (box that the phone is plugged into, which is in turn connected to the internet) work as routers and we could view both router's home pages through their ip addresses.

We first called Vonage customer support, and no matter what they suggested in the nearly 2 hour call, nothing worked.We found a solution that suggested changing the MAC address of our router. After looking at the settings of the Vonage box, we couldn't work out how to change the MAC on this, so we changed the MAC of the Linksys instead - and it worked. We could view our emails and website again.However, plugging the Vonage box back in resulted in us losing access to our emails and website again. The set up solution worked for about a day before the same problems came back.

So we again unplugged the Vonage phone device and just ran our two Macs from the Linksys router - all fine, for a bit.A couple of days later the emails and website became inaccesible again. In desperation I changed the Mac address of the Linksys router and we were up and running again.

This solution worked for another day or so, until the old problems arose again.Now, whenever we reset the Mac address of the Linksys, it works, but emails and the website become inaccesible sometimes as soon as half an hour afterwards, sometimes longer, but however long we can gain access to the emails for, we constantly have to stop to reset the router, then restart everything.We now know that its nothing to do with the Vonage phone, so I'm discounting that from the equation now. Also, we've just tried running each of our computers in turn when plugged directly into the modem via an ethernet cable. Interestingly, one machine works fine, and can access the emails and our website, but the other machine now can't access the email or the website, but loads all other sites fine. Is this significant?

We've been reading up on our problems again, and it has been suggested that the issues are being caused by the website/email server blocking our ip address and that we can solve this issue by having a static ip address instead of the dynamic one that Virgin Media assigns. As we are on a home broadband service, we understand that this isn't possible though. Surely, if Virgin reassigns ip addresses every session, our ip would be constantly changing, therefore if we were blocked by the website server, wouldn't it be more likely to be blocking a static one, not one that is constantly changing? And also, how come one of our machines can access the emails etc when directly connected to the modem, but the other can't?

Other solutions proposed have been:
-Get a new router
-Move our website to a new server
-Move our emails to a new server and access our own website through a proxy.