Daniel,
I don't get how that paid for resource deals with your question. I can make a different guess at what you are talking of and comment on that... if I am not helping please just ignore me.
It sounds like when you are at work your firm wants you to spend any computer time doing productive work for the company. It therefore blocks access to all manner of things not connected with work. You mention gambling and your own Web site. I expect social networking sites are blocked and so on too, as people waste so much time playing with such things when they are being paid to work.
If your Web site is something you should be getting paid to look at then you would normally just chat to your IT dept. and ask them to classify it as something that they allow. They will look at the site of course, to see what they want to classify it as. At present 'none' probably means they think it has nothing to do with their business/work.
If your Web site has nothing to do with work and you should not be looking at it whilst being paid to work then you may need to ask if there is a period of the day when these restrictions do not apply, like during lunch, or after 5pm... you may be in luck on that as at times folks will want to check their bank or book their holiday or pay a bill and some firms may allow it at certain times. Another way around this sort of thing is to use a smartphone or similar to look at your Web site.
You could go all the way and setup a hotspot using your phone and connect your computer to it or whatever. Most firms would consider firing someone who did that though to get around their controls designed to keep them working. Likewise with finding other ways of getting to your own Web site if your firm wants you just doing the work they pay you for.
As I say, please just ignore me if I am guessing wrongly or whatever.
Steve