I just had the same problem. The fan worked on only one speed, low. In my case I replaced the switch first. This gave me the lower three speeds. Then I replaced the resistor. I found it severly corroded and the connector burned, on the resistor and pigtail. replacing this part gave back all speeds. The resistor is extremely easy to get at and replace, under the dash next to the blower on the passenger side. Nothing else needs to be removeed to get at it. It has to harness plugs attached to it which can be removed by squeezing the release latch. The resistor is installed with two 8mm screws. I bought the resistor at auto store, the pigtail at the junk yard although I found them also available new at some stores. At the junk yard I looked through several cars before I found one with a pigtail which was not also corroded and burned so I expect this is a very common issue and one to go after first.
I found this on Repairpal Common problems page for you 97 ford escort. There are reports of failures of the CCRM or Constant Control Relay Module. The CCRM has relays and switches inside that control or provide power to the engine cooling fan, A/C clutch (to engage the A/C compressor), fuel pump and powertrain control module (PCM). Single switches or relays can fail internally causing a number of different symptoms including no start conditions (inoperative fuel pump or PCM), engine running warm due to inoperative cooling fan, or the A/C might not blow cold air.