Hi Michael,
To begin it would appear that you are not running an anti-virus program OR a firewall. BOTH are absolute MUSTS today.
Before you do anything else please go here
and download, install and update ONE of the FREE anti-virus programs that PP notes. You may choose any ONE of the three but you must choose one, install and use it. It will do no good whatsoever to clean this machine if you are not running an anti-virus program.
You also MUST use a firewall, the huge number of trojans found on your system is one of the ways you pay for not using a firewall. Either enable the built in Windows Firewall or download and install one of those noted by PP in the link above.
Once you have installed and updated the Anti-virus program of your choice I would like you to do a Full System Scan with it and have if fix/quarantine or delete anything found.

Next I would like you to run the Eset scanner again, but this time please have it clean whatever is found.
Save the log for posting here.

Next I would like you to download the latest version of Java which is 6 update 5. Your version is way, way out of date.
Go here to download the latest version. Please choose the Offline install and save it to your desktop so that you can find it easily.
After you have downloaded the java install pkg I would like you to go to Add/Remove and uninstall All previous versions of java that you find there.

While you are in Add/Remove also please uninstall the following;
Ad-Aware SE Personal
Coupon Printer for Windows
HOTLLAMA Media Player
LiveUpdate 2.6 (Symantec Corporation) (evidently a remnant of a previous Norton Anti-virus program which is no longer on the system)
You also should look there for SurfMonkey programs, allegedly will make your browser "for kids only" but it is most definitely Adware and something you DO NOT want on the computer. It will remind you to subscribe to their service every now and then. And displays a bunch of sponsor's logos in a sidebar. It MOST definitely is running on this computer. If you do not find it in Add/Remove then go to C:\WINDOWS\ and look for SurfMonkey. If you find it, delete it.

Once all above items are uninstalled then double click the java install program that you downloaded and install it. Once it is installed then go here to verify the install went well.

After you have done all of the above I would like you to run HJT again and place a checkmark next to the following entries if they still remain;

R3 - URLSearchHook: (no name) - ~CFBFAE00-17A6-11D0-99CB-00C04FD64497} - (no file)
R3 - URLSearchHook: (no name) - ~00A6FAF6-072E-44cf-8957-5838F569A31D} - (no file)
O2 - BHO: (no name) - {CB2ADFC2-80F3-4608-B9D8-10BE2A4E70D1} - C:\WINDOWS\system32\jkhhf.dll (file missing)


O4 - HKLM\..\Run: [SunJavaUpdateSched] C:\Program Files\Java\j2re1.4.2_03\bin\jusched.exe
O4 - HKLM\..\Run: [Alcmtr] ALCMTR.EXE
O4 - HKLM\..\Run: [58be37a2] rundll32.exe "C:\WINDOWS\system32\eotpitpu.dll",b
O4 - HKLM\..\Run: [g]eeV\mWhjlnspB] C:\WINDOWS\system32\qcntlkdn.exe DWram
O4 - HKCU\..\Run: [My Web Search Community Tools] "C:\Program Files\MyWebSearch\bar\1.bin\m3IMPipe.exe"
O4 - HKCU\..\Run: [Amrbrs] "C:\Program Files\Common Files\??crosoft\n?tepad.exe"
O4 - HKCU\..\Run: [wqif] C:\Program Files\InetGet2\stub109_4_0_4_0.exe
O4 - HKCU\..\Run: [Srro] "C:\DOCUME~1\HP_Owner\MYDOCU~1\CROSOF~1.NET\chkdsk .exe" -vt yazb
O4 - HKLM\..\Run: [ELNKProxy] C:\WINDOWS\surfmonkey\smproxy.exe

O8 - Extra context menu item: &Search - ?p=ZJxdm128MFUS
O20 - Winlogon Notify: qommmjh - qommmjh.dll (file missing)

Once you have placed the checkmarks then click the Fix Checked button.
Exit HJT.
Reboot the computer.
Run a NEW Malwarebytes' Anti-Malware Scan
Have it remove everything found. Save the log for posting here.
Then run a new HJT scan and save that log and post it here.
We can then decide what needs to be done next.
Judy