Hi Stan,
Firstly, if you keep to the pin names as used in Manual 1 then we don't have to go through the question/answer sequence of confirming which physical leg/pin you use.
Its a useful 'convention' which disambiguifies descriptions.
As BCJ wants you now to confirm; are you talking about "In2" (physical leg 5 as shown in the PINOUT diagram in Manual1) ?
Secondly, it is HIGHLY unlikely that you have a duff PICAXE. Obviously not impossible, but most faults where people question the chip usually find it's themselves to blame or they (or a 'friend') have damaged it.
Thirdly, with the 47R and 15K you should be easily OK; the voltage calc by Andrew is correct.
Lastly, you say 80%... is that using a multimeter? Or is that using BASIC code to test the 'logic' level of the pin.
Have you tried an 'Input' statement to make sure the pin/leg is an input?
Post your code and wiring diagram (aka 'schematic')
If you are using a multimeter, then take the PICAXE out of the equation - just connect your resistors and P/B switch and connect Multimeter.
If you are only getting to 80% of 5V (with P/B pressed) then you have something else going wrong.
Have you double-checked component values?
Have you checked resistance of switch (when closed)? I assume it is push-to-make?
(Was it hacked from Grandpa's 1954 radiogramme? Or bought from Ebay?)