How to check if roof has ice dam issue
You need to look up your county's regulations for builder accountability/warranty.  In NW Washington the rule was 6 years for discovery and 6 years to get it fixed.  Simply there was a 12 year warranty unless the contractor was savvy enough to put in his contract 'In Lieu of Blah Blah Blah' warranty, putting in his own 1 year warranty.

Hire a Home Inspector...someone who works FOR YOU to go through your home to find PROBLEMS.  This should have been done before you signed anything to purchase this home.  They will go through your home WITH you and make sure you make them explain everything to you, mainly cause you are paying them for the information.  They are so reasonable, worth every cent.  I hired one 8 years ago and the bill was $150 for a huge, 4,000 sq. ft. log home with daylight basement.  He had his office in his van and any question at all was available via computer to include State, county and city warranties.

I used to build custom homes so I know the ins and outs.  If there is a shortcut MOST contractor's will take it to make money. Sad and wrong but so true.
Who can you trust?  A Home Inspector!!  Again, check the regulations.  It might be that the original owners only have that warranty but then that goes into the 'discovery' aspect to finally end up with the real estate agent in fault.  The roof is a big big deal.  Yours looks rather yucky.  Is any of the insulation wet?  Looks like they left the old rafters and ship lap.  Ugh job.  Do you have composite for the skin of this roof?  Do you have gutters?  Where is it leaking?

Go hire an inspector, they are your best bet to solve this issue, whatever it is. If you ever sell this home you'd better have your ducks in a row or this problem becomes yours to solve. Inspector, courthouse records..did you hire this contractor in 2010? Get records from them as well regardless.