Will Costco or ZT upgrade my ZT computer that I bought at costco (which I am having a lot of problems with) from From Window Vista Home to Window 7? Has anyone else asked these questions of either Costco or ZT?

If you purchased this recently, last few months, there may well of been an upgrade offer with the machine, otherwise they will most likely charge you for this.
You will need to contact ZT as Costco as simply a retailer.