Hi GadgetGirl,
I work for one of those companies you named above (not supposed to say which one, since this is a personal message rather than official communication from the company. Plus, I don't want to get flamed by every Tom, Dick & Harry that ever had a problem with their credit card!
).
Anyway, you 'can' just buy swipe card readers at, for example, Sim Lim square or the internet but that doesn't get you anywhere, assuming your intentions are honest.
In order for you to process card transactions, you need to establish a business relationship with an 'Acquiring' bank. They 'acquire' transactions from you (e.g. when a shopper uses his/her card in your business, the swipe terminal sends the details to this bank, which in turn sends it to the shopper's bank (Called the 'Issuing' bank because that is the bank wich Issues the card to the shopper). The Issuing bank then authorises (or not!) the purchase and sends the reply back to the Acquiring bank, and then to your terminal.) If the transaction is approved, the issuing bank will then credit your account at the acquiring bank, and debit the shopper's account.
When you establish this acquiring relationship, the bank themselves will provide the terminal. Very surprised that DBS, Citibank weren't interested. Try walking into a business similar to your own, and ask them who is their Acquirer.
Hope this helps. Let me know.