If these tickets have not been used since the new biometric finger scans have been in place, then I see no problem with the OP using them. WDW may say the tickets are non-transferable, but unless you have not used them with the new finger scans, there is no way for them to prove who used them in the past. So the OP find out if your parents have went threw the finger scan before. If they have not, then I say use them & not feel guilty despite what others here say about having a guilty free conscience. If they have been used with your parents fingers have been scaned, then it looks like you won't be able to use them & you would need to purchase your own set of tickets, sorry.
Finally to the people who said not to transfer tickets between anyone even family members, who are you to tell the OP or anyone else what to do? Ticket transfering happens all time. Look at all the people selling used Park Hopper Passes on Ebay & all the discount ticket outlets in Orlando. I would say all those tickets they are selling, (the ones at the discount ticket outlets) were from guests who decided to sell them for cash & therefore they are selling used tickets. So basically selling old & used WDW tickets happens everyday & you can't stop the process, eventhough it's wrong.