Hi,
I have been through this on my fridge, however it is a little newer than yours. The board features are a little different but looking up your model, the ignition itself appears to be the same.
See page 17 of 37 this manual. The PDF says 17 but the book page is 16
http://www.manualslib.com/manual/461515/Dometic-Rm2607.html?page=17#manualThere are 3 parts that "might" have an issue. However before getting into those parts, insure the grounds are good, clean and the DC voltage check going to the control board is up in mid 12 volts area. Like 12.5 and up. I cannot find quickly the low end cut off but if your converter is on it should be 13.25 or above. Battery only is not that hard to get 12.5 if the battery is up. If you are in the 12.0 area, charge the battery.
The 3 parts to sort out are the igniter, the cable and the electrode. Page 17 tells you how to do this. If you pull off the high voltage cable from the igniter and fire up the fridge on gas mode, you should hear it snapping non stop for 45 seconds then it will time out on saftey. A snap of about once a second says it is working. If the snap is intermittent,(misses some then starts again) and the actual 12 volts to the igniter and ground are good, then odds are the igniter is going bad.
This sounds like what you are describing as you can light it with a match and it runs from there. This means the electrode and high voltage cable has a level of working as the remote flame sense is still working or it would be sparking all the time. And if the system re-ignites once it is up and running, then odds are high a weak igniter is the issue as once the unit if primes and hot, 1 or 2 snaps and it is up and going. It does not have to work as hard coming up cold. You did not says if it re-ignites once you lit it the first time. I'm assuming it is. If not, then need to drill deeper into this
If you are not getting a non stop, once a second snap,snap, snap that is problem one, a weak igniter can cause this.
If you are not electrically friendly, do not attempt this. Hope this helps and good luck.
John
2005 Ford F350 Super Duty, 4x4; 6.8L V10 with 4.10 RA, 21,000 GCWR, 11,000 GVWR, upgraded 2 1/2" Towbeast Receiver. Hitched with a 1,700# Reese HP WD, HP Dual Cam to a 2004 Sunline Solaris T310R travel trailer.