In case that fails, on first sight they seem to use pretty standard partition and raid formats and you should be able to recover the data from just the drives. ( for example https://www.synology.com/en-us/knowledgebase/DSM/tutorial/Storage/How_can_I_recover_data_from_my_DiskStation_using_a_PC )

edit: does "the NAS itself" exclude the powersupply? if not sure, you could try your old NAS+drives with the new powersupply, if compattible.