LA will not help as they no longer fully support the school but still support offsite backups and virus systems as the school pay them for these services separately. Previously they were under contract to look after the schools network + servers, hence LA installed servers but no longer.
I'd get the LA to look, could be the LDF has grown, could be a long disc queue length which point to a duff disc. Log it with them, if it's a duff disc you don't want to be wasting time waiting for people to post on a forum with ideas. Would take 10mins of a remote support session to find the problem rather, what is it now, half a day and count.