If I understand correctly, you have a Motorola Photon 4G phone. Is this phone rooted or not rooted?
1. Were you ever able to install Avast or Anti-Theft on this phone at any time in the past? If so, you need to uninstall Anti-Theft FIRST, then Avast Mobile Security.
2. Did you ever have another antivirus or security program on this phone in the past? If so, did you uninstall it prior to trying to install Avast?
3. Are you able to download other apps. from the Marketplace? If not, please try turning your phone off completely, pull the battery out of the phone, wait a minute, replace the battery, then reboot your phone and try to download something from the Marketplace again. If you are still having problems with the phone (downloading something from the Marketplace or any other problem), you should contact your phone provider where you got the phone for assistance if it is under warranty. If it is not under warranty, you may want to do a hard Master reset, but this will wipe everything from your phone (all Contacts, third party apps, etc. will be gone unless you have a way to back them up).
4. Also, for the Marketplace to be able to download, you need to have "Background Data Enabled" on the phone; you can disable it once you are done using the Marketplace if you like. Did the problem with not being able to download things from the Marketplace start before or after you tried to download Avast?