Good news. If you get to the last icon, it means you are very close to booting and very good chance Haiku will boot for you.
During boot icons, VESA driver is used. After rocket icon, native Haiku graphics driver takes over if found (ie: intel_extreme in your case). There was an issue with this driver and some 945G video chipsets (those found on Atom systems). Same problem you describe.
You should be able to boot into safe-mode unless you have a keyboard issue (which is not likely). You actually have to keep pressing SPACEBAR while booting and not hold it down. LEFT SHIFTKEY you actually hold down. Try SPACEBAR method because I have had best luck using that myself but both ways work.
Once in safe-mode, select to use fail-safe graphics driver + a specific video mode you want. After booting, you can search for and delete intel_extreme driver. That will make VESA driver the default for booting and running Haiku.
Recent nightlies have a fix for intel_extreme issue but introduce another graphics bug which may affect you.
Adding yourself as CC to proper bug will inform you of any changes and updates made to it. Trying to find the right ticket might require a little work. Fixing bug can sometimes take a very long time - years to get done.