It seems clear that the only source of goods for the South was from foreign countries. Lincoln mandated a Naval blockade on all goods coming by ship, which did take some time to become effective, but there is no indication that northern industries were in any way part of the blockade runners. A research paper on Northern Industry in the Civil War has some interesting content and one section has the following:
One body of evidence indicates that the war widened this sectional disparity by destroying the South's minute industrial base and expanding that of the North to prodigious dimensions. Statistics on specific industries provide what appears to be convincing proof. While the loss of the Southern crop produced a steep war-long decline in production in the North's largest industry, cotton textiles, its woolen industry enjoyed a 100% production rise during the conflict. The second largest consumer industry in the Union, shoes and leather, also enjoyed tremendous growth, thanks to army contracts that more than offset the loss of the Southern market. Other war related industries, especially firearms, gunpowder, and wagon manufacturing, grew rapidly on the strength of military contracts. Meanwhile, iron production in the North experienced a slump early in the war but boomed 1863-64, in the latter year reaching a production level 29% higher than that of the entire country in the busiest prewar year, 1856. The coal industry experienced similar growth, in 1861-65 enjoying an expansion rate 21% higher than that for the nation as a whole during the 4 years immediately preceding civil strife.
The whole article is in this link:
Northern Industry In The Civil War The article does seem to support that the notion that northern industries were supporting the "government" and people of the Union, with no mention of supporting southern interests. So, there is no indication that the North supplied anything to the South, but the premise that no company in the Union sold any goods to the South after 1861 still proves to be difficult to document.