Primary Hypothyroidism: This is the most likely diagnosis given the significantly elevated TSH level (66) and low free T4 (0.53) level. The free T3 level is relatively preserved, which can be seen in some cases of primary hypothyroidism, especially if the disease process is not completely advanced. The body may attempt to compensate for the low T4 by increasing the conversion of T4 to T3.

Subclinical Hypothyroidism with Recent Onset or Fluctuating Disease: Although less likely given the high TSH, some cases of subclinical hypothyroidism can present with fluctuating thyroid function tests, including periods of elevated TSH with relatively normal free T4 and free T3 levels.
Recovery Phase of Thyroiditis: In the recovery phase of thyroiditis (e.g., subacute, silent, or postpartum thyroiditis), TSH can be elevated as the thyroid gland recovers, and thyroid hormone levels may fluctuate.

Pituitary Tumor (TSH-Secreting Adenoma): Although rare, a TSH-secreting pituitary adenoma could cause elevated TSH and thyroid hormone levels. However, the low free T4 level in this case makes this less likely, but it's crucial not to miss it due to its significant implications.
Resistance to Thyroid Hormone: A condition where there is reduced sensitivity to thyroid hormones, leading to elevated TSH and thyroid hormone levels. The clinical presentation can vary, making it a "do not miss" diagnosis due to its potential for being overlooked.

Familial Dysalbuminemic Hyperthyroxinemia: A rare condition characterized by abnormal binding of T4 to albumin, potentially leading to misleadingly low free T4 levels despite normal or elevated total T4 levels. However, this would not typically cause an elevated TSH.
Thyroid Hormone Resistance Due to Transport Protein Abnormalities: Abnormalities in proteins responsible for thyroid hormone transport into cells could potentially lead to elevated TSH and altered thyroid hormone levels, though this is exceedingly rare and usually presents with more complex clinical features.