Dual core vs single core

My company provides online questionnaires for children, the site utilises Flash and SAPI 5 speech engine and when the child logs on they download a 0.5MB renderer and off they go.
We had a dedicated which was hosted externally and was a Server 2003 machine with SQL 2000 running on it with 100+ databases.  The spec of the server was 2.8GHz dual core Pentium P4 with 2GB of RAM, and it worked OK.  When a young person logged on Task Manager reported that the sqlservr.exe will go up to about 2% and the change to network usage is negligible.
The problems started when we fell out with the hosting company and moved elsewhere.  We got a server with the same spec as the previous one ie 2.8GHz P4 processor with 2GB RAM and Server 2003 and SQL 2000 standard edition (SP4).  The problem now is that whenever someone tries to logon to our site the sqlservr.exe process is shooting up to 90+% and is falling over altogether if more than 5 people try to log on at once, whch is a disaster when we used to have classrooms full of kids accessing our site at the same time.  Our programmers say that the code on both servers is identical, so the only cause of this issue can be the hardware, and the only difference between the 2 servers is that the old server had a dual core processor and the new one doesnt.  I cant believe that a dual core processor can be the difference between 90+% CPU usage and 2% CPU usage.  Please can somebody let me know if a dual core processor can make such a difference, and if this is considered unlikely, does anybody have an idea what could be causing this problem.
I asked my current hosting company to put a dual core processor in and they said the motherboard wouldnt support it, so possibly that may be a factor.
Please, please, does anybody have any ideas as to what could be causing such a difference in performance on 2 servers which barring a few minor things are considered identical.
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I think the problem is not the cpu but how SQL Server was configured.  A P4 2.8 should have no problem handling 30 normal users, let alone 5, and plenty of database servers get along on less powerful cpus.  Hardware is not the problem in this case.

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PilkyAuthor Commented:
This is what I thought, but I cannot find any difference between how SQL is configured in both servers.  Do you have any idea as to what part of SQL config I should look at?
Sorry, I'm just a hardware guy, I don't configure SQL Servers :-)  I should try taking that up.  I'm sure someone in the Microsoft SQL TA would know the answer to that.
PilkyAuthor Commented:
Thanks for your rather prompt help. As a last question, in your experience, can you expect a dual core processr to improve performance a lot in a site such as the one I have described? Or would the likely performance difference between dual core and single core be negligible?
A dual core will help if you have a single core that is near capacity.  If you expect more than 30 simultaneous users or observe that the cpu is reaching maximum utilization, a dual core will help.  Otherwise, a single core is sufficient.
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