For the purposes of this tutorial, I will assume that the old drive is /dev/sda and the new drive is /dev/sdb. Check these before you do anything, and adjust the commands appropriately. Also, make sure that you have a Windows installation or repair CD/DVD available.
1. Download and burn an Ubuntu CD. You want the 32-bit desktop edition standard CD (not alternate or DVD). You can follow the instructions to put this on a flash drive instead of a CD if desired.
2. Boot from the CD or flash drive in "Try without installing" (Live) mode.
3. Press Alt-F2 and type "gksu palimpsest" in the box that appears, then press enter.
4. Select the new drive in the left pane.
5. Near the top of the right pane, select "Format Drive".
6. In the dialog box that appears, select "Master Boot Record".
7. If it asks for confirmation, go ahead and confirm.
8. Create a new "Empty" partition spanning a little less than the entire drive.
9. Wait for all disk activity to stop, then close the window.
10. Open a terminal (Alt+F2 and type "gnome-terminal", then press enter)
11. Type "sudo dd if=/dev/sda1 of=/dev/sdb1" and press enter (the ones are important, they specify the partition number).
12. Wait for it to finish (it will take a long time, and there is no progress indicator), then close the window.
13. Press Alt-F2 and type "software-center", then press enter.
14. Search for and install GParted if it is not installed already.
15. Close the software center when the installation completes.
16. Press Alt+F2 and type "gksu gparted", then press enter.
17. Select sdb in the drop-down menu in the top right corner.
18. Right-click the partition in the list and select Resize.
19. Resize the partition to the size of the drive.
20. Click the green check to apply the changes.
21. When the operation completes, close GParted.
22. Press Alt-F2 and type "gksu nautilus", then press enter.
23. When the window opens, navigate to the partition that you used as D: in the left pane, select all the files in the right pane, then press Ctrl+C.
24. In the left pane, navigate to the new drive.
25. Paste the files wherever you want.
26. Repeat steps 23-25 for the partition that you used for E:.
27. Click the eject symbol in the left pane.
28. Turn off the computer (pressing the power button will bring up the menu).
29. When prompted to remove the CD, replace it with your Windows CD/DVD.
30. Remove the old hard drive, leaving only the new one.
31. Turn the computer back on, pressing a key at the "Press any key to boot from CD/DVD..." prompt if necessary.
32. Choose whatever option gets you to a command prompt.
33. Run the fixmbr command.
34. Restart your computer and remove the Windows CD/DVD.
35. You should now be back in Windows, running off your new drive, with all partitions merged!