I reinstalled HL2 recently and was still plagued by this message

    "Error 108: The local steam service is not running."  

Googling revealed nothing obvious. The steam forums were particularly unhelpful since the search term "108" is not long enough to be used. Despite this, I found this suggestion from the Steam website, again of no help.

The solution, in my case anyway was painfully simple. If Steam was installed to C:Program FilesSteam then it must be run from there and nowhere else. NTFS joins and substitute drive mounts made using the dos command subst will not do the job. Since I have a NTFS join (for the sake of convenience) which mounts "C:\Program Files\Games" as "G:" I was trying to run Steam via G: instead of from where it was installed.

Hope this helps someone.