What issue(s) are you encountering when you try to place an online order? Some banks / credit card issuers may need to be informed beforehand that the card will be used for international transactions, and they may (or may not) require some sort of limit to be imposed. I don't know if UK card issuers are more stringent than their N. American counterparts regarding card usage. You may want to contact your bank / card issuer to find out if there are any stipulations regarding its usage for online orders.
The problem with using your friend's card is that, for product warranties and disputes related to the goods received, they would need to be handled by him/her because the orders were placed under his/her name. You're unlikely to have any recourse unless the item(s) come with a gift receipt, and seeing as you're in a different continent, they may be reluctant to honour warranties or RMAs of said goods.
This probably won't help you much in determining what's permissible as far as carry-ons go, but it's worth a read: TSA - Permitted and Prohibited Items
. My guess is that if it's anything electronic or electrical in nature and it can't be tested when asked to do so at the request of security, they will err on the side of caution by confiscating the item(s) in question, i.e. they'll probably seize them all. You could ask an airport official upon your arrival to NY to determine if you can pack any PC components in your carry-on; if they say you can't, the next best thing would be your check-in luggage. Of course, TSA officials can open luggage randomly, and there's no guarantee that everything will be there when you return to the UK, but it's a better bet than packing it in your carry-on.