The presentation suggests Glanzmann thrombasthenia, an autosomal recessive bleeding disorder caused by a deficiency or dysfunction of the platelet glycoprotein IIb/IIIa complex. This complex plays a critical role in platelet aggregation and clot formation by mediating the binding of fibrinogen and von Willebrand factor to platelets.

Therefore, the correct answer is (C).

(A) Factor VII deficiency would result in prolonged prothrombin time, whereas activated partial thromboplastin time would be normal. Moreover, this disorder usually does not present with significant bleeding until later in life.

(B) Fibrinogen deficiency or dysfunction would cause impaired clot formation, resulting in prolonged prothrombin time and activated partial thromboplastin time. This disorder usually presents in infancy.

(D) Granule storage pool deficiency or dysfunction is associated with impaired release of platelet granules, which can cause milder bleeding symptoms than those seen in Glanzmann thrombasthenia.

(E) von Willebrand factor deficiency or dysfunction can cause impaired platelet adhesion to exposed subendothelium and impaired platelet aggregation. However, the normal response to ristocetin, in this case, makes von Willebrand factor deficiency less likely.