Cpu Dual Xeon
Cpanel (only 1 domain)
Bandwidth 2000 GB
Data Center USA/CANADA
24x7 chat support
Disk Space 40GB
Linux CentOS 5.3 (Final)
Server for vBulletin script optimised
Do you know what your current resource usage is? I am assuming host monster suspended your service / contacted you because of the resources your site used?
Your budget and specs are in a pretty okay range and you should be able to find a server within the $60 range like that. However cPanel is a very expensive software license so I doubt you will find cPanel included for that price range. If you can afford to add $20 you should be able to find what you are looking for easy.
If you can forego the use of cPanel for a single site, you can meet your budget. Maybe even consider a different control panel called DirectAdmin which would only be about $10 may be very close to fitting into your budget.
Yes, I'm using vbulletin script powered site and when online users become more than 200 my site shows cpu quota limit error or database error and low speed. I'm going to transfer my site to a dedicated server with this rule:
A good rule of them about resources (just for vB)...
0 to 100 = Shared will do.
100 to 200 = High VPS will do.
250 to 500 = Dual Xeon will do.
500 to 700 = Dual Xeon (2GB) with 1 web front end.
750 to 1000 = Dual Xeon (2GB) with 2 2GB web front ends.
1000+ = Dual Xeon (4GB) with 3 2GB web front ends.
The best thing you can get with your $60 budget is from interserver.net It's 2 core ATOM server with cPanel its $59/month
This would be your best bet at the moment for cPanel to be included. Note that I have no experience with the above mentioned and cannot personally recommend them however it does seem to be one of the few places that will fit your budget.