Can a judgement prevent a cash sale

Ask the broker(s) involved. A broker with experience in the building can tell you whether or not you should bother trying to buy. If you go for a condo then it won't matter.

First of all, do you realize that besides a BK, an open judgment (which I presume is meant an "unpaid judgment") is probably the most serious red flag for a cooperative board? Judgments last for 20 years and a judgment lien, if it is docketed in the County where you are purchasing the property, would be a lien on your co-op shares. Alas, there is no Co-op board in the world that would approve a sale to you under these circumstances. Now, if by "old judgment", you mean a paid judgment, it will depend how long ago it was and how much it was. Nevertheless, it will be a huge red flag. If you have a good explanation, it was a modest amount, it took place a long time ago and your income/assets are otherwise high it could mitigate the impact somewhat. However, you will still probably face an uphill battle. Now, if the judgment is unpaid, then your Co-op will deny you because you are an idiot, to wit: why would anyone attempt to do an all cash co-op purchase and not pay off the judgment first?? I will give you the benefit of the doubt and presume you are not that stupid.

P.S.: there are million other reasons that they will deny you if the judgment is unpaid. The above barely scratches the surface.