Are you SURE the original 10K resistor is not to GROUND?
i.e. 10k keeps RESET low, reset uC drives it high when 5v rail is above brown out voltage!
Hence, removed reset uC = RESET (cause 10k pulls reset low) and 100R mutimeter to 5v brings line high (Vreset is 5v * 9.9/10)
You swapped resistor to 1K, 100ohm still just enough to get out of reset (Vreset is 5V * 900/1000)
Then fitted 270ohm, now, of course your 100Ohm "mutimeter shunt" isn't enough, and you need 30Ohms!!
Check this!!!
PS, units current has gone up because you have a 270Ohm short to ground!