Its been used at least an average amount of times..
10 times a year for 10 years = used 100 times.
10 times a year for 20 years = used 200 times.
hard to know for sure, but clearly waaaaaayyyyyy more than 4 times!
Condition also looks average for its age, not great, not bad.
without some Ariens or Tecumseh tag numbers, its hard to get a fix on its age.
Ariens made several 1236 models in the 924000 series:
The Ariens 1960's and 1970's Sno-Thro info site.
Seven different 1236 models between 1988 and about 2004.
Based on the graphics and the style of the dash panel, this is probably an early to mid 1990's machine, about 20 years old..
if you could get the numbers from the tags, snowblower and engine, we could nail it down to an exact year.
One might think, when it comes to snowblowers, "the bigger it is, the more expensive/valuable it is"..but that really only applies to *new* snowblowers..Once they hit that 15 to 20 year old mark, exact age has little importance..a 40 year old Ariens can be worth the same, or even more, than a 20 year old Ariens of similar specs, depending totally on condition and previous owner care.
And, for older machines, being at the top of snowblower food chain, in terms of size and power, can be a distinct disadvantage! for many buyers and many regions, because the machine is simply far too big for their needs.. the massive size can make it *less* valuable than smaller machines of similar vintage, because demand for the monster machines is lower in all areas except those regions with greater than average snowfall amounts..
So! $350? not bad..probably a bit high, unless you live near one of the large east coast cities.
(it would be very helpful if you would tell us where you live!

just a city and state is fine..)
$250 is probably good if everything works..and again, only if you really need the size!

If you live in Virginia, you really dont want this machine..It will not do well in 2-inches of slush. this is a machine for 1, 2 and 3 foot snowfalls, and several of them every winter.
Scot