Hello Leosghost and incrediBill,
Unfortunately there's no 'backup account'. The suggestions you both make to narrow the number of causes down are very welcome and I'll use them when contacting the hostingprovider tomorrow morning.
The software I was using at the time the problem occured were a texteditor and a FTP client. The cookies and cache were both already cleaned, but that didn't help.
I'm gonna use a proxyserver to continue my work, after all a slowish connection is always better then no connection at all.
And to answer you last question, when the PHP files are referenced under a domain name on this particular server, they still don't work.
Although I'm not to keen on hosting websites for clients, a few of them are on this same shared server, but under their own unique domain. All these sites work perfectly, as long as they're not viewed from my ISP IP-number.
Tomorrow I'll increase the pressure on both my ISP and hosting provider to come with an anwser on what's wrong and a good solution. When I know I'll post both the cause and the solution in this thread for future reference.
Thank you all for your efforts on your free (that's what I hope, at least) sunday!