The first statement you suggested is fine, but as you noted, it isn't the shortest nor smoothest sentence.
Given that there are only two problems and only one suggested action, there is not a lot of ambiguity in the last formulation:
If you are having problem X or problem Y please contact Z.
However, the clarity of the sentence depends heavily on how the problems are worded! If the problem statements are very long, it might be good to start over with a new "if". For instance
If you have problems restarting your computer or configuring your router, then call our tech support
is very readable, whilst
If you are having problems restarting your computer due to the power button being stuck and the computer being too small for you hands, or opening the window, then please call our tech support
is a rather obnoxious statement.
Also, when you are using different formulations*, an extra "if" is essential:
If you are having problems opening your door, or if you are unable to find your keys, please contact the police
*As mentioned in the comments below, this is not quite precise enough. When using several different verb phrases, you need to separate them and using an extra 'if' can help with that.