First of all, lets narrow down the problem. What you need to do is see if it IS the alarm causing this. More than likely, the alarm brain will be up under the dash somewhere. It will be a small black box around 3"x4" with a long plug on one side. If you find this, unplug it and check to see if your speedo starts working, mirror lights, ect. I've never heard of an alarm causing problems with a speedo but when it comes to the door locks and lights.... yeah you could have a problem. It could be something as simple as bad contacts with the wiring or a brain gone bad. Both could be due to age but without knowing how it was installed, you never know. Check to see if unplugging the alarm helps and let me know. Don't just pull a fuse, you need to unplug the long white plug with all the wires in it. If that happens to help, then either leave it unplugged or replace the alarm with a new one installed by a qualified pro. Is there a big problem with theft out on Hawaii?