The key difference is that Best Buy is a corporation, and you are probably thinking of a painter who does not do business as a corporation. (They might be a sole proprietor, for instance.)
As far as I know, the $600 rule isn't about Form W-9 itself. Rather, the rule is that when your business pays more than $600 for services, you may be required to file Form 1099-MISC. One of the boxes on that form asks for the recipient's Taxpayer Identification Number (TIN), so you have to get that from them somehow, and a common way (though not the only way) is to give them a Form W-9 and ask them to fill it out and return it to you. Form W-9 also asks the recipient to state whether they are subject to backup withholding; if they are, or if they won't give you their TIN, then you have to withhold taxes from the payment and send it to the IRS, reporting this on the 1099-MISC as well.
Now, if you look at the section "Exceptions" on the 1099-MISC instructions:
Payments for which a Form 1099-MISC is not required include all of the following.
Generally, payments to a corporation (including a limited liability company (LLC) that is treated as a C or S corporation). However, see Reportable payments to corporations, later.
Best Buy is a corporation, and none of the exceptions under "Reportable payments to corporations" apply when you are paying them for computer repair services. Therefore, you do not have to file a 1099-MISC when you make such payments to Best Buy. As such, you have no need to get their TIN, and therefore no need to ask them to fill out a W-9.