Disk /dev/sda: 160.0 GB, 160041885696 bytes
255 heads, 63 sectors/track, 19457 cylinders
Units = cylinders of 16065 * 512 = 8225280 bytes
Disk identifier: 0xd65316e1
Device Boot Start End Blocks Id System
/dev/sda1 1 4382 35198383+ 7 HPFS/NTFS
/dev/sda2 4383 18422 112776300 7 HPFS/NTFS
/dev/sda3 * 18814 19457 5172930 c W95 FAT32 (LBA)
/dev/sda4 18423 18813 3140707+ 5 Extended
/dev/sda5 18423 18788 2939863+ 83 Linux
/dev/sda6 18789 18813 200781 82 Linux swap / Solaris
You have about 5Gb of Windows FAT32 (sda3) and about 3Gb for Linux on the extended partition (sda4) divided into two logical partitions for swap and the system. 3Gb is quite small. You could just combine the FAT32 with the Linux to make 8Gb, but even that may not suit you in the log term. If you just want to try Linux out and then make more space later, that would be fine, but it might be good to make this a little bigger now. Are you using that extra Windows FAT32 partition for anything? I think not, because with what you have described, I think that is the result of your attempt to put the partitions back together. So, here is my recommendation:
Start up the usb and run the installer that you originally used to repartition. Use this one, because you already know that it is not going to give you problems. The problem is one I've had twice and it is caused by a mix of kernel, parted, and the way your BIOS has your hard drive set. Your setup is probably ok since you didn't have the problem before, but I'd hate to see you try a new installer that had the bad combination. I know that folks who have not experienced this will think I'm nuts, but I was surprised to have it happen the second time to me using remix and a toshiba nt205 a month ago. The fix required getting the restore disk and an external cdrom in order to restore windows so that the windows boot sector could be rewritten. It is a royal pain on a netbook and for me was costly. Plus you overwrite windows. All that would have been needed was fixboot, but the restore disk does not have it. An XP install disk does have it; so it is an easy fix with that. Lots of words here, but I do not want to be the cause of trouble. So, if you feel secure, you can just go with the eeebuntu installer, or you can take the extra care and use the one you originally used.
When it gets to the partitioner highlight partition 6 and delete it. Do the same with 5, 4, and 3. Then resize 2 and take another 10-20 Gb off that. Then you will have 18-28 Gb of free space. Make all of that into an extended partition so that you can make 2 logical partitions on it. Then make the swap like you did before and the rest of it into the Linux partition.
Install on the new partition with eeebuntu. If you have only one usb stick you would have to first continue with the install of remix, and then put eeebuntu on the usb stick and install over remix.