Users report that the server has become non-responsive.
What are the possible explanations, and how do you check out each one. Please answer in the order in which you judge it to be most reasonable to check this out. A terse columnar answer is acceptable.
This is not an "easy to answer" question. I'm afraid until some work is done on each of the components of the system the answer smells of "it depends on your application". Here goes with some rather general steps of where to look.
1) Which users are complaining? Is the whole work force? Just those in one location or users who are physically remote. Consider the type of connections in to the database. Are they on the office LAN or connecting via dial up. In the user community are these users complaining about a single part of the application or all of. Be careful here, some people may just be complaining because they want to. You need to verify their complaint. This may provide you some information about where to look. Be aware some people will be suffering from the effects of the problem rather than the problem itself.
2) Identify all the components of the system. Consider breaking the whole application into a series of components, and investigating the performance of each component. You will need to consider the load on the operating system of each server (web, application, database etc). Has the data or application grown beyond the original design specification? You may need assistance from the people who support your network, web servers, application servers, development teams, DBAs and analysts. Possibly the project managers who initially delivered the project. If the problem is critical, they will normally be interested in helping out.
3) Once the components have been identified, install a monitoring regime. Have your original specifications of what each component should be capable of delivering and compare the delivered performance with the specification. For ASE use sp_sysmon and sp_monitorconfig to gauge the DBMS performance.
4) Begin tuning those components that are suffering. Sometimes performance can be improved by changing configuration parameters, ASE can certainly be tuned; for others, you may need to add hardware. Normally changing the application can provide a large increase in performance, but at realitively high cost - design, coding, testing and documentation needs to be redone.
5) Continue monitoring, was the change sucessful, did the performance improve, is the system performing acceptably? If the answer to the last part is "yes", then you've probably solved the problem (for now). Believe me, 4 and 5 is normally an iterative process. Solving one problem normally reveals another.
I'm sorry this is so vague, but a question like "It doesn't go fast enough, what do I do now?" doesn't really offer an opportunity to provide further investigation.