The notion that ENIAC was the First Computer is really open for debate. Atanasoff's machine at Iowa State[1] had DRAM and binary logic in the late 30's. Zuses[2] machines in Germany during WW2 were similarly advanced. In the article they specify the 'first programmable' computer, but when you're moving wires around, that's hardly a distinction imo.
[1] http://en.wikipedia.org/wiki/Atanasoff%E2%80%93Berry_compute...
[2] http://en.wikipedia.org/wiki/Konrad_Zuse