Well, first of all, you made a common panic mistake when infected....you downloaded and installed another antivirus, thinking 2 is better than 1. This is a bad idea on a clean PC. On an infected one, it can make a bad situation worse, when the 2 AVs start flagging each other as infected or wrestling over rights to infected files. So for starters, I would remove either MSE or Kasper, take your pick, and make sure to run the removal tool from the vendors website of whichever product you remove, to clean it all up, AV programs never want to fully remove correctly, even less so when installed with another AV simultaneously.
As far as logs, one of the stickies states no HJT logs on this forum, so that idea is out.
From what you posted though, it looks like a Java exploit. My suggestion would be to Run a scan with MSE or Kasper, depending on which one you keep, let it quarantine (NOT DELETE unless there is no other option, the Temp files cant be quarantined for example) what it finds, then follow by installing and updating this>>http://www.malwarebytes.org/products/malwarebytes_free , do a Quick scan with it and see if anything is left. Once that is all done, remove all Java from your system (and reinstall it, if you use it, many have Java but never need it, making it pointless risky baggage).
If after all that, the same infection symptoms return, I would think you have a rootkit then. But cross that bridge when you come to it, for now just go with the above steps.
A few days ago, my computer started acting up. We have 4 accounts on our families computer, mine is the only one having problems so far. My sister downloaded FrostWire last year, I think. I uninstalled it and I went through and deleted all the files I could find. When I logged on the Calculator was pulled up, I closed out of it and it would come back. After about 10 minutes they started multiplying every time I tried closing them. Then random ads would pop up on their own like QuestionSpider, Local.com, 2oosk.com, Adbrite, Plus.Google.com, IntornetDotOrg, ********e, and Depleted.org. Internet Explorer closes on its own, but Google Chrome is fine. The ads stopped after I downloaded Microsoft Security Essentials and ran it a couple of times. The calculator is still popping up though. I keep scanning the computer with Kaspersky AV 2012 and MSC but neither of them are finding anything else so far besides these that MSC removed so far:
Items: containerfile:C:\Users\Chelsey.Mae.RobertMCoyle-PC\Frostwire\Torrent Data\iTunes Store Top 10 Songs (USA 2012)\We Are Young (feat. Janelle Monae) - Fun.mp3
Items: containerfile:C:\Users\Chelsey Mae.RobertMCoyle-PC\Frostwire\Torrent Data\Fun - We Are Young (ft. Janelle Monae)\Fun - We Are Young (ft.Janelle Monae).mp3
Tech Support Guy System Info Utility version 18.104.22.168
OS Version: Microsoft Windows 7 Home Premium, Service Pack 1, 64 bit
Processor: Pentium® Dual-Core CPU E5400 @ 2.70GHz, Intel64 Family 6 Model 23 Stepping 10
Processor Count: 2
RAM: 5885 Mb
Graphics Card: Intel® G45/G43 Express Chipset, -1281 Mb
Hard Drives: C: Total - 381551 MB, Free - 268835 MB; D: Total - 564118 MB, Free - 563964 MB;
Motherboard: ASUSTeK Computer INC., CM5571
Antivirus: Microsoft Security Essentials, Updated and Enabled
I have the logs from DDS, HiJack This, and Malware but wasn't sure if I should post them