OHHHHH! Sorry, ummm, yeah I would try what 'remain' suggests. Right click, Duplcate, rename one as Skype1 or something, then try starting one and then the other...beyond that...if it's using the same ports on the computer...not sure if it will Work. I know I've used one skype account on the imac, one onthe pc, one on the macbook pro, and one on the netgear skype phone all at once on the same router, no issues.
Just not on the same computer.
I'll give it a try tonight, and post back if I succeed.
Brian