I have a problem with an Ubuntu installation. I know, I could just go to askubuntu, but I figured, with the helpful community here, I could just ask here as well.

I bought a new laptop, which had Linpus Lite installed.
I decided to install Ubuntu on it. I downloaded the ISO, created a bootable USB stick, then installed Ubuntu on the laptop. When it asked how I want to install it, I chose the option to install it alongside Linpus.
The intallation completed successfully, however, the laptop seems to be able to boot only when the pendrive is plugged in. If I reboot it without the pendrive, I get a screen telling me that no bootable drive was found.

Searching for this error, I found solution. Thus, as instructed by the [url=http://members.iinet.net.au/~herman546/p20/GRUB2%20Bash%20Commands.html#install_update_and_repair]linked guide, I tried to do a sudo grub-install /dev/sda. However, then I got an error about being unable to find the canonical path of /cow (then I tried looking for solutions for this, but the solutions I found didn't work).
Then I reinstalled Ubuntu, specifying the partition where I was about to install Ubuntu to be mounted as / and instructing the installer to install the boot loader on dev/sda, but this didn't solve the problem.
Then I installed and used the boot-repair tool, which did some work, confirmed that boot has been repaired, but the problem still hasn't been solved.

Is there any way to repair my installation? Or should I just reinstall Ubuntu once more, this time telling it to erase everything and install itself that way? Maybe delete all partitions and create just one partition (+one for swap) manually?

Yes,personally I would start all over again and tell it to erase all.
You can partition after it's all done and working to your satisfaction.

Thank you, I will try that and let you know how it worked out.

Now I've tried it, and it still produced the same error. Checking the contents of that one partition which has been now created, I saw that there IS a boot/grub folder there, so it *should* work.
Then I checked in BIOS and saw that boot type was set to UEFI. I changed it to Legacy, now it doesn't give me a "No bootable drive" message, but all I get is a blank, black screen.
UPDATE: I have reinstalled once more after changing to Legacy, and now it is booting fine from HDD.