Can't say that I've had, or heard of, this exact problem, but the very first thing that I would check is that ALL of the grounding cables from the battery negative post are in place, and in good condition. One large cable should go to the frame and then on to the engine block; a smaller cable should go to the inner fender or the radiator support; and especially check that a grounding strap is present from the firewall to the engine. That last is commonly forgotten after engine work or engine swaps, and it not being there can cause a lot of screwy symptoms. The blower motor is a large, "noisy" draw, so I can see it not having a good circuit path* causing an issue.
* Always look at electrical as having a "circuit path" from battery positive to the component and then back to battery negative; the grounding side is as just important as the powering side.