I mean, when I will to buy a new Laptop, what I have to know about hardware, if I want to have no problem with OpenBSD? Maybe there ate a list of Laptops or something like that?
The problem with lists is that they are either incomplete or out-of-date. The problem is compounded by the fact that manufacturers change components depending upon what deals they strike with their suppliers, so once a list is compiled, six months later it is not only no longer relevant, but factually incorrect. Case in point, I purchased a HP mini netbook a few weeks back partially because there was a post on OpenBSD's misc@ mailing list saying they had absolutely no problem with this particular model. Wireless worked fine. I purchased the same model, & everything worked but wireless. In comparing dmesg(8) output posted on misc@ & what I had on my netbook, the BIOS was significantly newer on mine, & some key components (ie. wireless) were different. I kept it, & it's not a bad little netbook, but the kernel doesn't recognize the Broadcom wireless chipset at all. At least, for now. Development on OpenBSD is ongoing, so it might be supported later.
It is common that wireless support will be sporadic. Wireless vendors in particular are very nervous about releasing information on their chipsets, & because they aren't open, this hampers the Open Source Unix-like operating systems be it the BSD family or Linux. Vendors will also cripple some chipsets & label them with different model numbers. This also hampers some wireless drivers from working correctly too.
Another problem with laptops/netbooks is that vendors "improve" models, & release them with different model numbers. As another case in point, OpenBSD works fine on the original (from what I can piece together...) Acer Aspire One, however, Acer has made newer AAO models which are slightly larger, & with different components. The original model is no longer on the market. I have seen where X freezes if the touchpad is used at all on one of these newer models. The only option is to plug in a USB mouse. Obviously, there is an issue with this particular touchpad & the mouse driver.
Sure, we would all like to have no hassles or problems, but this is unrealistic in the Open Source world. If you don't want unexpected surprises, take a live CD with you to the store & see what is reported in dmesg(8) output. Maybe a store won't let you boot a live CD. If not, go somewhere else, or make sure you understand the return policy upon purchase. I would also highly recommend studying the misc@ archives to see what other people are using. From what I have read on misc@, others attempting to run OpenBSD on Lenovo's netbook (I don't recall the model numbers...) haven't been exceptionally pleased, but then, satisfied users wouldn't necessarily be posting.
...I'd recommend switching to one of the other BSDs instead.
This is an option, but there is another alternative still with OpenBSD. Your message didn't indicate which flavor of OpenBSD had been installed, but you could try -current. Although OpenBSD 4.6 was just released in October, the code base was frozen several months ago. -current is now many months past 4.6-release. This may be an option you may want to explore, but read Section 5.1 of OpenBSD's official FAQ such that you are aware of the implications of running -current. Personally, I find -current to be highly stable, but there are occasionally issues which I have to resolve. Some people freak out when things don't compile or they have to dig deeper into the documentation in order to troubleshoot. -current isn't for everyone.
But how can I know WHERE is problem?
The first place to look is at the dmesg(8) output. Yes, I understand that the system crashes on boot, but bsd.rd obviously worked. Perhaps a live CD would allow you to copy the dmesg onto a USB drive. Even assuming you get that far, the next thing to do is study the crash(8) manpage carefully. In contrast to other non-BSD Unix-like alternatives, OpenBSD's manpages actually provide useful information in a digestable form.