This sounds similar to what happened to me.
Crysis played flawlessly on my ATi 3870 until I got to the on deck carrier battle. It would just lock up within minutes of getting on deck.
That video card still works but there is something not quite right with it. Once I upgraded to a 260 GTX that same battle scene worked fine.
I got the chance to do a quick test after "validating" the installation. the same thing occurs with the same error from windows concerning running out of memory with the usage at that point at about 76%. I don't think it is the video cards since it is the system memory that is the problem. I am still trying to find out why or what is causing this.
I did find a ref in the event viewer to a problem with missing/corrupted windows file/s. So late last night I went and did a full defrag then ran both "Disk Check" and "System File Checker". System file checker did in fact find some corrupted/missing files and repaired them. I'll just have to get a chance to try it out again. I guess if this doesn't work the next step will be to remove and reinstall Crysis completely.