If you want to run three monitors on a single card you will have to go with an ATI/AMD Eyefinity compatible card. The downfall is, you will have to run one of the monitors off of a display port connection, which will require an adapter so you can use it with your DVI monitor. If you screens are running at around 1920x1200 or lower, than you can get away using a cheap display port to DVI adapter. However, if you are running like 2560x1440 which a lot of 27" monitors are these days and I'm guessing you are since HDMI doesn't work, you will need a much more expensive display port to dual link DVI adapter.
As for your HDMI troubles, it isn't working for you because it's running what is essentially a single link DVI signal, and so the cable physically can't support the bandwidth you need in order to run anything higher than 1920x1200.
Honestly, your best bet is going to be to check your computer to see if it has two PCI-E slots, and just run two video cards. (Once again which model is best will depend on what you do.). The cheapest option will be to find out what kind of card you have and just buy a low end third one (as long as you aren't gaming on all three monitors), to support the third monitor. So if you have a Nvidia card pick up something like a Geforce 210 or if you are running ATI/AMD something like a HD4350.
Sorry I can't give you something more specific. If you can provide some more specific details such as what you use the computer for, model numbers on the 27" monitors, and some basic PC specs, I can give you a more specific suggestion of "Buy this, or Buy that".