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.