Welcome to the forums, cosmofur. 
An analysis of your HJT log shows the following problems :
We couldn’t detect any active process of a firewall on your system. Possible reasons:
(1.) You are using the windows firewall or a hardware firewall.
(2.) You are using a firewall of an unknown vendor.
(3.) You are using a firewall, but for unknown reasons it is disabled
(4.) You don’t use any firewall at all.
We recommend you to use a firewall. Download and install one or activate windows xp´s own firewall.
You have 2 active antivirus scanners which is not at all recommended as they will conflict with each other causing less protection rather than better protection. This may have also contributed to the computer infection.
O1 - Hosts: 172.16.1.205 backups
Unknown URLs should be fixed. Unknown entries within the HOSTS-file should be fixed.
This one might be OK. http://www.robtex.com/ip/172.16.1.205.html
O1 - Hosts: 65.199.31.21 www.studyforalz.com
Must be fixed! http://www.robtex.com/dns/studyforalz.com.html
O2 - BHO: (no name) - {8A9D74F9-560B-4FE7-ABEB-3B2E638E5CD6} - (no file)
Unnecessary (deactivated) entry that can be fixed.
http://www.spyandseek.com/Search.php?search_for=8A9D74F9-560B-4FE7-ABEB-3B2E638E5CD6&search=SAS-Search (numbers 4 & 6 on the list)
O2 - BHO: (no name) - {eab1d8e7-1d9b-4ad0-8da9-3bfca6d506f6} - (no file)
Unknown application. Unnecessary (deactivated) entry that can be fixed.
O2 - BHO: (no name) - {F0626A63-410B-45E2-99A1-3F2475B2D695} - (no file)
Unnecessary (deactivated) entry that can be fixed.
http://www.spyandseek.com/Search.php?search_for=F0626A63-410B-45E2-99A1-3F2475B2D695&search=SAS-Search (numbers 6 through 10 in list)
O4 - HKLM..\Policies\Explorer\Run: [RTHDBPL] C:\DOCUME~1\Steven\LOCALS~1\Temp\soxmenawcr.tmp
Should be fixed. Sign of a trojan dropper. http://www.systemlookup.com/Startup/20964-lsass_exe.html
http://www.sophos.com/security/analyses/viruses-and-spyware/trojtattersa.html?_log_from=rss (see More Information tab)
[b]O16 - DPF: {CF38E898-0A6B-11D6-83C6-0080AD7D6076} (NPRemvuPluginControl) - http://172.16.1.21/common/NPRemvu.cab[/b]
Check if you know this site and fix it if you do not. Unknown ActiveX-Objects, or ActiveX-Objects from unknown sites should always be fixed.
O21 - SSODL: laloyifuj - {2c0e253f-89b5-4a6d-b71a-66421a9bca78} - (no file)
O21 - SSODL: lunujowit - {d34ac6ef-3e33-4db7-9470-0f0eac9dea33} - (no file)
O21 - SSODL: hiwunapan - {f19d3934-0a6f-4025-9bd5-ae61dd65e343} - (no file)
O22 - SharedTaskScheduler: tokatiluy - {2c0e253f-89b5-4a6d-b71a-66421a9bca78} - (no file)
O22 - SharedTaskScheduler: kupuhivus - {d34ac6ef-3e33-4db7-9470-0f0eac9dea33} - (no file)
O22 - SharedTaskScheduler: gahurihor - {f19d3934-0a6f-4025-9bd5-ae61dd65e343} - (no file)
Research on the above 6 entries suggest that there might be a Vundo infection.
O23 - Service: JZTJBUZV - Unknown owner - C:\DOCUME~1\Steven\LOCALS~1\Temp\JZTJBUZV.exe (file missing)
Unnecessary (deactivated) entry that can be fixed.
Overview of running tasks :
smss.exe
System task
Session Manager Subsystem
winlogon.exe
System task
Microsoft Windows Logon Process
services.exe
System task
Windows Service Controller
lsass.exe
System task
Local Security Authority Service
svchost.exe
System task
Microsoft Service Host Process
svchost.exe
System task
Microsoft Service Host Process
svchost.exe
System task
Microsoft Service Host Process
aswUpdSv.exe
Virusscan
Avast Anti-Virus Component
avgchsvx.exe
Virusscan
AVG Internet Security
avgrsx.exe
Backgroundtask
avgrsx.exe
avgcsrvx.exe
Virusscan
AVG Internet Security
ashServ.exe
Virusscan
Avast
spoolsv.exe
System task
Microsoft Printer Spooler Service
ACService.exe
Backgroundtask
ArcSoft Connect Service
avgwdsvc.exe
Backgroundtask
avgwdsvc.exe
svchost.exe
System task
Microsoft Service Host Process
jqs.exe
Backgroundtask
Java Quick Starter Service
CommandService.exe
Unknown task
Unknown task http://www.bleepingcomputer.com/startups/CommandService.exe-24500.html
mdm.exe
Application
Machine Debug Manager
NMSAccessU.exe
Backgroundtask
NMSAccessU.exe
nvsvc32.exe
Application
NVIDIA Driver Helper Service
svchost.exe
System task
Microsoft Service Host Process
UAService7.exe
Backgroundtask
SecuROM User Access Service
avgnsx.exe
Backgroundtask
avgnsx.exe
ashMaiSv.exe
Virusscan
Avast Anti-Virus Component
ashWebSv.exe
Virusscan
avast! Web Scanner
Explorer.EXE
System task
Microsoft Windows Explorer
smax4pnp.exe
Application
Soundmax agent
svchost.exe
System task
Microsoft Service Host Process
avgtray.exe
Backgroundtask
avgtray.exe
ashDisp.exe
Virusscan
Avast AntiVirus
ctfmon.exe
System task
Alternative User Input Services
GoogleUpdate.exe
Backgroundtask
GoogleUpdate.exe
GoogleUpdate.exe
Backgroundtask
Google Updater
hpqtra08.exe
Backgroundtask
Hewlett Packard Imaging
GoogleCrashHandler.exe
Backgroundtask
Google Update
GoGear_Vibe_DeviceManager.exe
Backgroundtask
GoGear VIBE Device Manager
hpqimzone.exe
Driver
HP Imaging Module
TurbineLauncher.exe
Unknown task
Unknown task http://www.tallemu.com/oasis2/file/turbine__inc_/turbine_launcher/turbinelauncher_exe/1275093
hpqSTE08.exe
Driver
HP Imaging
SyncBackPro.exe
Unknown task
Unknown task http://www.tallemu.com/oasis2/file/2brightsparks_pte_ltd/syncbackpro/syncbackpro_exe/2682553
dllhost.exe
System task
Microsoft DCOM DLL Host Process
AAWService.exe
Anti Add/Spyware software
Ad-Aware 2007 Service
AAWTray.exe
Backgroundtask
AAWTray Application
winlogon.exe
System task
Microsoft Windows Logon Process
HPZipm12.exe
Driver
HP Taskbar Utility
Ad-Aware.exe
Virus http://www.backgroundtask.eu/Systeemtaken/Taakinfo.php?ID=778
RBOT-SO WORM!
iexplore.exe
Application
Microsoft Internet Explorer
iexplore.exe
Application
Microsoft Internet Explorer
HijackThis.exe
Application
Merijn Hijackthis