Q:

Why did The Doctor become Gollum-like creature when The Master increased his age to 900 years?

In the season 3 finale, The Master suppressed the regeneration ability of 10th Doctor and increased his age to 900 years which made him a Gollum-like creature.
From Last of the Time Lords episode transcript:

MASTER: What if I suspend your capacity to regenerate? All nine hundred years of your life, Doctor. What if we could see them?
  (The Master retunes his screwdriver and zaps the Doctor again.)
  MASTER: Older and older and older. Down you go, Doctor. Down, down, down the years.
  (Finally the convulsions end. The Doctor is no longer sitting in the wheelchair.)
  MASTER: Doctor.
  (A tiny creature with big eyes, rather Gollum-like, peers out from the otherwise empty clothes.)

At old age, The Doctor regenerates (like The War Doctor), but this time his generation ability was suppressed. So, the situation was just like 11th Doctor in The Time of The Doctor when he didn't have regeneration energy to regenerate. In The Time of The Doctor, when The Doctor was going to die of old age (after living probably 900 years), he wasn't Gollum-like creature.
If I am asking in chronologically wrong order, the question may be: Why didn't The Doctor turn into Gollum-like creature in The Time of The Doctor?

A:

It's not really clear that the Master was simply accelerating the natural way the Doctor would have aged over a much longer period, as opposed to manipulating his biology in some artificial way to "age" him in a way that would not be normal for a Time Lord. From the transcript of the previous episode, "The Sound of Drums":

MASTER: Oh, how to shut him up? I know. Memory Lane. Professor
  Lazarus. Remember him and his genetic manipulation device? What,
  did you think that little Tish got that job merely by coincidence?
  I've been laying traps for you all this time. And if I can concentrate
  all that Lazarus technology into one little screwdriver? But, ooo,
  if I only had the Doctor's biological code. Oh, wait a minute, I do.
(He opens a large metal briefcase.) 
MASTER: I've got his hand. And if Lazarus made himself younger, what
  if I reverse it? Another hundred years?

Then he ages the Doctor for the first time, which is done by just giving David Tennant old-man makeup instead of using CGI. Although this could be consistent with the Master just accelerating his aging, I think it's equally consistent with the possibility that he's altering the Doctor's biology to create a type of aging that would be "unnatural" for Time Lords, or perhaps a reversion back to the way some earlier stage in Time Lord evolution would have aged. There is reason to think that Time Lords have altered their biology since discovering time travel, like how we know from River Song that

 River acquired non-human DNA (and the ability to regenerate) because
 she was conceived while the TARDIS was in the Time Vortex, despite
 both her parents being human

or like the "Rassilon Imprimatur" which was described in "The Two Doctors" as "a kind of symbiotic print within the physiology of a Time Lord", and which was said to be necessary to operate a time machine. So the Master's laser screwdriver could have removed some of these newer biological features, which could be involved in both regeneration and in the slowing of Time Lord aging within a single incarnation. 

A:

There have been several instances, where the doctor has been aged by external influences. The biggest instance of artificial ageing I could find, was indeed in the episode The Leisure Hive, in which that specific regeneration of The Doctor was aged by 500 years for a brief moment:

The Fourth Doctor is briefly aged 500 years in The Leisure Hive, leaving him an old man but still active.

Still you are completely right, The Doctor was only aged about 100 years by The Master's laser screwdriver, which should be no problem at all as The Doctor stayed  approximately 900 years on Trenzalore fighting off external threats to the very end. 
I have three theories:

The laser screwdriver was set to degenerative aging and what we
saw was an extremely bad aged Time lord, can happen to the best of
us ;)
The Regenerations age differently
This was something written by Russel T. Davies and the other instance was written by
Stephen Moffat and they simply overlooked that bit

