Marian,
As far as I am aware you haven't posted details about your search for your granfather on Rootschat (just the search for your father). Even if you can't get his service record, it's amazing how much of his time in the Army during WW1 can be reconstructed provided that you know a little bit about him, for instance his unit, and ideally his army number(s). Have you found his medal index card? These have all survived, so if there isn't a MIC for him, that may indicate that he didn't serve outside the UK. The main problem with MICs comes when your subject has a fairly common name and it's hard to identify his specific card among many others of the same name.
And it's not strictly true to say that the MOD and or TNA have 'lost' any service records. As you know roughly two thirds of all the WW1 service records (up to 1920) were destroyed in a fire caused by a German bomb in WW2. If you grandfather's was among them then whatever you were told in 1984 didn't come from those documents but from another source. Depending on his regiment, you may find that places like regimental museums hold additional records such as enlistment books and tracer cards which have survived. Also some pension records (created by the Ministry of Pensions, not the War Office) have survived so if he was entitled to a disability pension there may be a record of this. Also around 5% of the medical records for soldiers hospitalised during the war have survived so again somewhere worth checking. Although soldiers are rarely referred to by name in the war diaries, it is usually possible to use these to recreate a fairly good picture of where and when a unit was in action and when it wasn't. Contrary to popular belief most soldiers spent more time away from the front trenches than they did in them.
Another way of approaching your research, provided that you know the person's Army number* is to search for other soldiers with numbers close to your subject and see if you can find their records. Often these men will have served alongside your subject and so if their records have survived, you can build a picture of what your subject's time in the Army might have looked like. This is particularly true of the First World War where men were encouraged to join up in groups who all knew each other or came from the same local area or place of work. These units were called Pals' battalions.
*Soldiers' numbers prior to 1920 were in fact Regimental numbers and so different units might have men with the same number, so this method only works for men of the same unit. You can often work out when a man enlisted based on when his number was issued - more details
here
