This is not a support request as I've already solved my problem. However I'm posting the solution in the event that others come across the issue in the next few hours/days. Forgive me if this is in the wrong section.
Running IC² v1.62 with RedPower Machine V2.0pr4d causes a conflict.
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java.lang.RuntimeException: RedPowerCore: BlockID 250 exists, autoAssign is disabled.
at forge.MinecraftForge.killMinecraft(MinecraftForge.java:332)
at eloraam.core.Config.getBlockID(Config.java:114)
at RedPowerMachine.initialize(RedPowerMachine.java:121)
at mod_RedPowerMachine.initialize(mod_RedPowerMachine.java:48)
at mod_RedPowerMachine.ModsLoaded(mod_RedPowerMachine.java:20)
at ModLoader.init(ModLoader.java:832)
at ModLoader.AddAllRenderers(ModLoader.java:189)
at afq.<init>(afq.java:80)
at afq.<clinit>(afq.java:9)
at net.minecraft.client.Minecraft.a(SourceFile:265)
at net.minecraft.client.Minecraft.run(SourceFile:648)
at java.lang.Thread.run(Unknown Source)
--- END ERROR REPORT 527012a9 ----------
Block 250 exists. This means we need to go into the IC2's config and change blockMachine=250 to something else. You can find the config in %appdata%/.minecraft/config/IC2.cfg
Open the file up in your favorite text editor, find the blockMachine=250 line and change the 250 to an ID that is not being used by anything else.
The way I found an ID that wasn't being used was to load up minecraft without IC², but with NEI loaded. Then I looked through the item list for an available ID. I then did the same with IC² loaded and without RedPower Machine just to confirm that the ID wasn't being used.