Without outbound protection there is nothing stopping any malware one your system downloading more of the same, I know XP's firewa (half a firewa ) doesn't and it is likely your hardware firewall does either.
The ashAvast.exe should be in the C:\Program Files\Alwil Software\Avast4 folder, you could try a repair of avast. Add Remove programs, select 'avast! Anti-Virus,' click the Change/Remove button and scroll down to Repair, click next and follow. You need to be on-line to do this.