Are quantum computers at least build able? Assuming a highly unrealistic where you basically have unlimited money to burn.
Is it possible to a build a size scalable quantum computer?
My premise is that I often read tha people have a made a single qubit transistor etc... but the system needs to be cooled with liquid helium to remain operable and so is not really practical. What if someone had the cash to buy cold liquid helium for arbitrarily large systems. Do we then have at least size scalable systems that could in theory become large full size Quantum Computers if someone paid for the coolant?
 A: The problem isn't coolant. MRIs use liquid helium, for instance, and they're clearly practical. The problems are things like coherence times (making qubits last a while without errors), performing gates quickly, bringing many qubits together so you can do large operations, etc. There are currently a number of candidates for what a scalable quantum computing architecture will look like--superconducting qubits, trapped ions, Rydberg systems, topological qubits, linear optical elements. Different architectures have different problems: ions have amazing coherence times, but the gates are not very fast. Superconducting qubits are potentially easily scalable (you can circuit-print them) but their coherence times are currently very bad. 
People with "highly unrealistic" money (Google, Microsoft, Lockheed, the US government) are currently funding research to make these architectures more scalable. We are not yet at the point where money itself is the only lacking material--even if you had enough money to buy all possible materials, there are still years of focused research efforts between the current state of the art and a useful quantum computer.
EDIT: Comments and other answers have mentioned D-Wave. I'll just note that they are...controversial. It's not widely accepted that this represents a legitimate quantum computer, or a type of quantum computer which is provides any advantage relative to classical computation.
A: First of all, I’m a bit remote from this topic, so please take what is below with care.
At the present time (October 2015) there is no known fundamental phenomenology which forbids the construction of a quantum computer. At the same time, there is no known phenomenology which contradicts quantum physics. Rather, there is a common belief that quantum physics is the only description of the world. As such quantum physicists usually heal their theory when finding new phenomenology. They usually put some patch on their theory to be sure no-one will contradict quantum physics. In the past they did this for spin and co. (spin-orbit and hyperfine structure, …)  for instance. Actually, a good work-in-progress is decoherence, which can be shown to emerge from quantum physics. (*) So in principle nothing forbids you to construct the quantum computer you’d like to.
Now if you consider the world as a finite ressource, scalability problems pop in.
You have to define criteria for a good scalability, as e.g. the amount of energy you need to put in order to get an outcome, how many physical qubit you need to implement a logical one, the space they require,… Some implementations have been ruled out (mainly quantum optics) since they consume too much place and energy, but I do not remember the exact criteria used, and more certainly it was propaganda from solid-state physicists... (just to warn you this topic is at the edge of physics and industry, where propaganda emerges). Anyways, the problem of scalability is an actual problem, since many basic properties of quantum mechanics in qubits have been demonstrated (coherence, manipulation, preparation, coupling between two qubits, … in addition with dramatic increase of the coherence times and fidelity). 
An almost good criteria is of course how the space $S$, energy consumed $E$, and number of physical qubit $P$ needed, … scale with the number of logical qubits $n$. If they scale exponentially: $\left(S,E,P\right)\sim e^{n}$, then clearly an other architecture where $\left(S,E,P\right)\sim n$ has to be preferred. That's kind of the reasoning in this branch of research, but I just invented the criterion, and there exist more refined ones for sure. For space scalability, more certainly a nice criterion would be $S\sim 1$
: adding a logical qubit does not require more space, but that's certainly just a dream !
I found this week the following paper

Resource Costs for Fault-Tolerant Linear Optical Quantum Computing, Ying Li, Peter C. Humphreys, Gabriel J. Mendoza, and Simon C. Benjamin
  Phys. Rev. X 5, 041007 (open access journal)

where they calculate the number of physical qubits required to implement a given (surface) code using the linear optics quantum computation computer. To appetise you, the APS wrote a short highlight in Physics (the journal). 
I regret there is no review cited in this paper, but perhaps it already gives you a good starting point to get answer to your question. Have fun ! 
(*) Funnily enough, mathematicians do the contrary: they believe classical mechanics is the fundamental one, and they understand quantum mechanics as a perturbation of the classical physics (crudely speaking). This is called the deformation quantisation, but it’s not the topic of this question. It is not clear at the present time whether the two approaches are equivalent. Here we just want to enforce the idea that there is no known limitation towards quantum computation.
A: The problem is that a quantum computer must be kept from becoming entangled with other objects.  Each time it is read, or receives input, or even with the passage of time, it can decohere and lose its quantum properties.  The Institute for Quantum Computing at the University of Waterloo in Canada is one resource with a website where you may keep up with developments in the field.  Wikipedia provides this Timeline of Quantum Computing that may be used as a portal to what has been accomplished.
