Can you have 2 wireless routers connected?

Yes.

You can plug one router into the other (with a long Ethernet cable).

(Most routers won't do wireless Bridge Mode)

The routers need to have different IP addresses.

You can give them the same SSID if you put them on different channels (1, 6, or 11) and use the same wireless password and disable DHCP on the new one.

You cant do it the way you are thinking

But you can do it the way Paul P suggested, however you should also turn off NAT on the second router as well as DHCP (also remember - you must not plug the second router into your phone socket)

In place of the long ethernet cable you can use homeplugs, but these will probably cost as much as a range extender

but have you tried the following

Where is the router connected to the phone line (I assume you are connecting to the internet via the phone line)

Is it downstairs with the pc?

If so - have you tried moving the router upstairs to the other phone socket and connecing the pc via wireless?

Moving the router upstairs should give better range/signal strength

Sorry - no

Very few wireless routers can be converted to act as a repeater

Here is what you need

http://www.dlink.com/products/?pid=741