First of all, lets look at the requirements for windows 1, it is an 8 bit computer with 385k ram memory.
So, if you have space, it is possible. DIY computers are really not something difficult to make. 
displayed here is a board with transistors, that together makes a 4 bit computing processor.
In simplified terms, this is basicly it, the challenge is to make 2^3 times more efficient and smaller the occilator (crystal frequency) can be increased and so small it fits in inside the area of a coin. But that wasn't one of the requirements.
Now the problem is, to make it out of something that looks like this: 
It would take a lot of space.
A fast google of DIY RAM Memory shows that something similar could be made, fairly easy, where the true challenge is to make it small and modular. But given the means to extract the resources the area to build it, (i mean Boeing production size buildings), it could be done.
Regarding the running speed, i'm afraid i'm not experienced enough in that area, to know what speed it would run but it would largely be controlled by the switching capabilities of the transistor but i could not find the datasheet of the "first transistor" but a general purpose transistor has a switching capability of about 300 MHz.