Transformers are generally considered to be the costliest assets in a power network. The lifetime of a transformer is mainly attributable to the condition of its solid insulation, which in turn is measured and described according to the degree of polymerization (DP) of the cellulose. Since the determination of the DP index is complex and time-consuming and requires the transformer to be taken out of service, utilities prefer indirect and non-invasive methods of determining the DP based on the byproduct of cellulose aging. This paper analyzes solid insulation degradation by measuring the furan concentration, recently introduced methanol, and dissolved gases like carbon oxides and hydrogen, in the insulating oil. A group of service-aged distribution transformers were selected for practical investigation based on oil samples and different kinds of tests. Based on the maintenance and planning strategy of the power utility and a weighted combination of measured chemical indicators, a neural network was also developed to categorize the state of the transformer in certain classes. The method proved to be able to improve the diagnostic capability of chemical indicators, thus providing power utilities with more reliable maintenance tools and avoiding catastrophic failure of transformers.