On a 1997 Blazer if the heater only blows cold air what might be the problem?

more than likely your heater core is clogged. GM's extended life anti-freeze can become very gummy after 2years. The simplest thing to do is to back flush the heater core. There are two heater hoses going to it [located on the passager side fire wall]. Remove the clamps and hoses from the heater core and simply stick a running garden hose one of the nipples. If water doesn't come out of the other nipple in a few seconds, move the hose to the other nipple. Chances are that you will get a nasty glob of slime coming out. Repeat the process several times until you only get clean water coming out in both directions. The heater core is now clean and you may reconnect the two hoses. Start car and allow some temperature to build up. You should find a nice warm heat coming from the heater now.