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It's takes over a minute to load a simple non-graphic Wordpress site. It's so slow the site that it would be unusable for the user.
There are *many* things that can cause a site to be extremely slow loading; what is the url for the site that you are talking about?
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I got one email back which stated that Dreamhost had a load problem and my server was being rebooted and should be back up shortly. It's more than 24 hours later and its still slow.
What is the load on the server where that site is hosted?
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All I get from Dreamhost tech support are emails saying we know its more than 24 hours since you contacted us - be patient we will get back to you as soon as we can.
That seems to indicate that they acknowledge receipt of your support requests, and *will* respond to you when they have a constructive response. It may well be that some further investigation is indicated, and they may need some time to accomplish that. 
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When you are on a shared host does this mean that you are not guaranteed any level of performance - a heavy user on the same server you are on can bring your sites to a halt?
Yes, it pretty much *does* mean that (and the TOS makes that pretty clear). That said, *my* experience with DreamHost over the last 10 years has been that, while there are occasional glitches that need attention, DreamHost's performance levels have been very high for what I pay.
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Dreamhost has some extra cost options that guarantee you some space and time. Why do I need to pay extra for something I thought I was already paying for.
It sounds like you really didn't understand *what* you were paying for. The DreamHost PS offerings guarantee you exclusive use of "N" amount of CPU and RAM, and the shared plans *share* those resources.
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If there is a user whose use is so heavy that it loads the whole server down shouldn't his usage be throttled down rather than bringing all of the other users on the server down?
Absolutely! It sounds to me like that *may* be what is happening on your server, based on your reported response from DreamHost Tech Support., and it sounds to me as though they are looking into the situation.
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Why am I not getting what I paid for. In response to my tech tickets all I get are automated responses that say we know its been 24 hours since you contacted us but hold on we'll get back to you just as soon as we can.
It sounds to me as though you *are* getting what you paid for. You have the ability to submit tech support requests via email, you have had "real person" responses as well as "automated responses" when you are "in the queue". DreamHost has indicated repeatedly that they *try* to respond to all tech support requests within 24 hours, but the never guaranteed that would be the case. You could have paid for a higher level of support response (callbacks on older higher level plans and as an option on the newer shared hosting plan).
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What are your experiences with other hosts? Dedicated servers? Virtual Servers? Any recommendations?
My experiences have varied greatly with other hosts; they all have "warts" of some kind or another. Other shared host have done no better (and most have done much worse) that DreamHost when it comes to basic service level, and none of them have been as flexible and powerful as the DreamHost custom web panel/shell combo. There is a reason I keep all my sites that are suitable for shared hosting on DreamHost, and have for years - they are simply the best deal going, over the long haul, in *that* type of hosting.
Dedicated servers are more expensive, and require more expertise to manage - I like having the basic infrastructure managed for me the way DreamHost does it. Virtual servers can be great, but they are also more expensive. It's all about your requirements.
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I'm on high speed cable and all of the other sites load quickly so its not a question of my equipment.
Fair enough, but that's not particularly relevant in the situation you have described - your equipment can be fine while still having routing issues (though I doubt that is the case). It very much sounds like you have an overloaded server, and that *can* be fixed -though it sometimes takes a little time for that to get worked out.
It's also possible, particularly with WordPress" that even with "few users", the site itself is part of the problem. The ready availability of all manner of plugins that do, or attempt to do, all manner of things means that two different WordPRess sites with the same available resources can respond in hugely different ways.
I've seen WordPress, and other, sites grind to a complete halt over things as simple as a slow response from Google analytics, a slow RSS feed parser, or inability to "grab" content form elsewhere on the net in a timely manner - happens all the time. Even major media portals have their sites sometimes rendered "unusable" by their own ad networks crappy performance.
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In fact one of the people I'm working with has his site, which has been up for several months and has far more users on a $6 Hostgater shared plan and he's getting much faster performance.
Yep! Folks' experiences *will* vary greatly, though that statement alone is pretty much meaningless without seeing both of the sites. I wonder if that would still be the case with identical sites that are running on identically loaded servers?
I can tell you are frustrated, and if the delays to get help from support are just more than you can bear, then you may well be happier with a different host. I can only speak from *my* experience with DreamHost and other hosts, and I'm more than willing to give DreamHost time to "sort it out" when something is amiss in exchange for the "total package" they offer ... YMMV.
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All the best,
All the best to you too!
--rlparker