donperla:
I was considering buying the UNO if it would solve my problem.
As I said already, you can use an Uno to upload .hex files to your ATtiny13A. However, if you're buying something solely for that purpose I don't think the Uno is the best choice. Much better is to buy a dedicated ISP programmer. The best one is the USBasp, which you can get for $2.33 USD w/ free shipping from China:
I prefer the 6 pin version since the Arduino boards use the 6 pin ICSP header. They also sell 10 pin versions and 6 pin to 10 pin adapters but I prefer not to deal with that unless I have a board with a 10 pin programming header.
The Arduino as ISP is a good option for someone who needs an ISP programmer and already has a spare Arduino board on hand.
donperla:
According to my communications with Microchip (who now owns AVR) I would have to buy an AVR ICE programmer at $130.00.
That's just the product they sell that you can use for this purpose. They didn't want to mention that there are other products for a fraction of the price. That product is what you would need for on-chip debugging but to buy it only to use as a programmer is overkill.