Hi apricot,
Please do not be offended by my comments. Here is an algorithm I would try when troubleshooting. First, though, we need more information.
What kind of computer is your dedicated computer? What OS is it running? Please give the specific one. What are your other computers? How much RAM is on the "server" computer? Is this wireless or wired? If wired, are you using 5e or 6? What are you using for a switch? 100Mbs or 1000Mbs? You say other things can get to the Internet. What other things? How much bandwidth do you have? These are important questions.
I wasn't a big fan of 6.0.10, but keep in mind that many people uses it, and it works for them. So, maybe it isn't the program but a combination of things. I think too many people assume it is the software. Was it working prior to three months ago?
The first thing I would do when there is an issue with software is upgrade. If you have an upgrade available, then I would install that asap. Also, how fast is AC on your server computer? Is it slow like the rest? If it is fast, then the issue is the network and not the computer.
The second thing I would look at would be the network. Cabling, switch, etc. If AC is working well on your server, then get a small, inexpensive Linksys 1GB switch and connect one computer to the server directly. Or use a crossover cable. This gets everything out of the way. If that computer is fast, then agaain, it is a network problem.
How do your browsers work on the bad computers? I don't think removing a computer will speed things ups.
Try these things and get back to us.