SQL Query suddenly slow --- how to test if its network or hardware (memory) issue?
There is not just a DBA but also a SysAdmin question.  Although, there are some basic DBA tools you should have in use to help you out.  


Slow query monitoring:  most databases have tools that allow you to monitor SERVER SIDE for slow queries.  Your system could be indexing, re-allocating memory and a myriad of other server side functions that could interfere with the speed of your queries.  Slow query monitoring will help you start drilling down and isolate.
Basic logging:  Make sure your server date is correlated with your local time (as in Germany +8 from US PST) to make it easy to look up your logs.  I often just (I use Linux based systems) run a tail -f on appropriate logs until the slow queries surface or note times of slow queries and then run through the logs.
Basic network network monitoring:  Setup a constant ping to your server(there are also plenty of bandwidth monitoring tools) that can be setup to alert you for slow traffic between two points as well as longer ping times.  


There are different indicators based on your operating system that will show memory issues such as page faults.  Memtester for Linux will stress test your memory and all of it when you direct it to.  Memory issues can be sporadic as not all memory is used at all times so access to bad memory can be intermittent.